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Central  University  Library 

University  of  California,  San  Diego 
Note:  This  item  is  subject  to  recall  after  two  weeks. 

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CI  39  (1/91) 


UCSD  Lib. 


AN    INTRODUCTORY   LOGIC 


THE  MACMILLAN  COMPANY 

NEW  YORK   •    BOSTON   •    CHICAGO 
SAN   FRANCISCO 

MACMILLAN  &  CO.,  Limited 

LONDON   •    BOMBAY   •    CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  Ltd. 

TORONTO 


AN 


INTRODUCTORY  LOGIC 


BY 


JAMES   EDWIN    CREIGHTON 

SAGE   PROFESSOR   OF  LOGIC  AND   METAPHYSICS  IN   CORNELL 
UNIVERSITY 


THIRD  EDITION;  REVISED  AND   ENLARGED   WITH   THE  ADDITION 
OF  NEW  PROBLEMS  AND  EXAMPLES 


Nefo  gork 
THE   MACMILLAN    COMPANY 

LONDON :   MACMILLAN  &  CO.,  Ltd. 


1051 


1919 

All  rights  reserved 

/to 

C8  4X 

8  C  R  I  P  P  S    IN 

OF   OCEAf 
VWtVSR^ITY 
LA  JO 


COPYRIG 


t  ON 

APHY 
FORNIA 
CALIFORNIA 


1900,  1909,     \ 
By  THE  MACMILLAN  COMPANY. 


Set  up  and  electrotyped.     Published  September,  li 


Norfaoob  p«gs 

J.  8.  dishing  Co.  —  Berwick  &  Smith  Co 

Norwood,  Mass.,  U.S.A. 


PREFACE 

This  volume  is  intended  primarily  as  a  text-book  for 
college  students,  and  grew  out  of  my  lectures  on  Logic 
to  undergraduate  classes  in  Cornell  University.  It  aims 
at  being  both  practical  and  theoretical.  In  spite  of 
the  obvious  deficiencies  of  formal  Logic  as  a  theory  of 
the  nature  of  thought,  I  am  convinced  that  it  is  one 
of  the  most  valuable  instruments  in  modern  education 
for  promoting  clear  thinking,  and  for  developing  criti- 
cal habits  of  mind.  J.  S.  Mill,  speaking  in  the  Auto- 
biography of  the  discipline  which  he  received  from  work- 
ing logical  exercises,  expresses  the  following  opinion : 
"  I  am  persuaded  that  nothing,  in  modern  education,  tends 
so  much,  when  properly  used,  to  form  exact  thinkers,  who 
attach  a  precise  meaning  to  words  and  propositions,  and 
are  not  imposed  on  by  vague,  loose,  or  ambiguous  terms." 
Although  in  treating  the  syllogistic  Logic  I  have  followed 
to  a  large  extent  the  ordinary  mode  of  presentation,  I  have 
both  here,  and  when  dealing  with  the  Inductive  Methods, 
endeavoured  to  interpret  the  traditional  doctrines  in  a 
philosophical  way,  and  to  prepare  for  the  theoretical  dis- 
cussions of  the  third  part  of  the  book. 

The  advisability  of  attempting  to  include  a  theory  of 
thought,  or  philosophy  of  knowledge,  even  in  outline,  in 
an  elementary  course  in  Logic,  may  at  first  sight  appear 
doubtful.  It  seems  to  me,  however,  that  this  inclusion 
is  not  only  justifiable,  but  even  necessary  at  the  present 
time.  Psychology  is  no  longer  a  '  philosophy  of  mind ' ; 
but,  under  the  influence  of  experimental  methods,  has 
differentiated  itself  almost  entirely  from  philosophy,  and 


vi  Preface 

become  a  'natural'  science.  As  a  natural  science,  it  is 
interested  in  the  structure  of  the  mental  life, —  the  char- 
acteristics of  the  elementary  processes,  and  the  laws  of 
their  combination,  —  and  not  primarily  in  the  function 
which  ideas  play  in  giving  us  knowledge.  It  is  clear  that 
psychology  does  not  undertake  to  give  a  final  account  of 
all  that  mind  is  and  does.  It  belongs  to  Logic  to  investi- 
gate intelligence  as  a  knowing  function,  just  as  it  is  the 
task  of  Ethics  to  deal  with  the  practical  or  active  mental 
functions. 

The  practical  question  still  remains  as  to  whether  this 
side  of  Logic  can  be  made  profitable  to  students  who  have 
had  no  previous  philosophical  training.  I  am  well  aware 
of  the  difficulty  of  the  subject,  but  my  own  experience 
leads  me  to  believe  that  the  main  conceptions  of  modern 
logical  theory  can  be  rendered  intelligible  even  to  ele- 
mentary classes.  Of  the  incompleteness  and  shortcomings 
of  my  treatment  I  am  quite  conscious ;  but  I  have  en- 
deavoured to  make  the  matter  as  simple  and  concrete  as 
possible,  and  to  illustrate  it  by  means  of  familiar  facts 
of  experience. 

For  a  number  of  the  practical  questions  and  exercises, 
I  am  indebted  to  Professor  Margaret  Washburn  of  Wells 
College  ;  others  are  original,  or  have  been  collected  in  the 
course  of  my  reading.  I  have  also  taken  a  number  of 
arguments  from  the  examination  papers  of  different  uni- 
versities, and  from  various  works  on  Logic,  especially 
from  Jevons's  Studies  in  Deductive  Logic,  from  the  little 
volume  entitled  Questions  on  Logic  by  Holman  and  Irvine 
(2d  ed.,  London,  1897),  and  from  Hibben's  Inductive  Logic. 

In  writing  the  book,  I  have  been  under  obligation  to 
a  large  number  of  writers  and  books.  My  heaviest  debt 
is  doubtless  to  Bosanquet,  and  perhaps  next  in  order  I  am 
under  obligations  to  Mill,  Jevons,  Sigwart,  and  Bradiey. 
I  have  also  derived  help  from   Minto's  Logic,  Deductive 


Preface  vii 

and  Inductive,  the  chapter  on  '  Reasoning '  in  James's 
Principles  of  Psychology,  J.  H.  Hy slop's  Elements  of  Logic, 
and  from  other  works  to  which  reference  is  made  through- 
out  the  book. 

My  colleagues  in  the  Sage  School  of  Philosophy  have 
kindly  aided  me  from  time  to  time  with  advice  and  encour- 
agement, and  I  have  also  received  valuable  suggestions 
from  other  teachers  of  Logic  with  whom  I  have  talked 
and  corresponded.  In  particular,  I  wish  to  express  my 
obligations  to  my  former  colleague,  Professor  James  Seth, 
who  read  nearly  all  of  the  book  in  manuscript,  and  to 
Dr.  Albert  Lefevre,  who  kindly  assisted  me  in  reading 

the  proofs. 

v  J.  E.   C. 

Cornell  University, 
August,  1898. 


PREFACE    TO    THIRD   EDITION 

The  present  edition  represents  a  somewhat  thorough 
revision  of  this  book,  which  had  remained  substantially 
unchanged  since  its  first  publication,  eleven  years  ago. 
Changes  of  more  or  less  importance  have  been  introduced 
into  every  chapter ;  new  paragraphs  have  been  added  to 
many  of  the  sections ;  and,  especially  in  the  Second  Part, 
many  of  the  sections  have  been  entirely  rewritten.  Chap- 
ter XIII.  of  the  old  text,  on  the  "Problem  of  Induction," 
has  been  expanded  into  two  chapters ;  and,  throughout 
this  Part,  an  attempt  has  been  made  to  bring  the  treatment 
of  the  various  inductive  methods  into  closer  relation  with 
a  general  philosophical  theory.  The  chapter  with  which 
the  text  formerly  closed,  "  Rational  and  Empirical  Theories," 
has  been  replaced  by  one  entitled  "The  Unification  of 
Knowledge."  It  has  seemed  important  to  conclude  the 
discussion  of  the  nature  of  thought  with  some  statement 
of  the  meaning  and  function  of  the  main  categories  which 
experience  involves,  and,  in  this  connection,  to  indicate  in 
a  general  way  the  necessity  of  a  philosophical  interpreta- 
tion of  the  results  of  the  special  sciences.  The  number 
of  problems  and  examples  of  reasoning  to  be  analyzed  has 
been  more  than  doubled  in  the  belief  that  fresh  material 
of  this  nature  will  prove  welcome  to  teachers  of  the  subject. 

The  two  purposes  of  an  introductory  course  in  logic 
which  were  emphasized  in  the  preface  to  the  first  edition  — 
to  afford  discipline  in  thinking  and  to  furnish  an  introduc- 
tion to  philosophical  studies  —  have  thus  been  kept  in  mind 


Preface  ix 

in  the  present  revision.  The  Third  Part  of  the  book  pre- 
sents an  elementary  account  of  knowledge  from  the  devel- 
opmental standpoint.  The  conceptions  there  treated  in 
a  somewhat  systematic  way  are,  however,  introduced  from 
time  to  time  in  the  earlier  chapters  to  modify  and  interpret 
the  results  of  the  older  logical  theories.  It  will  be  found 
that  the  more  theoretical  considerations  have  generally 
been  printed  as  separate  paragraphs  in  smaller  type,  and 
may  therefore  conveniently  be  omitted,  if  thought  desirable, 
when  the  time  devoted  to  the  subject  does  not  allow  a 
consideration  of  all  the  topics  dealt  with  in  the  book. 
These  paragraphs  are  usually  intended  merely  to  suggest 
further  problems  t«_>  the  student,  or  to  furnish  a  text  to  the 
teacher  for  explanation  and  elaboration. 

I  am  indebted  to  many  of  my  colleagues  who  have  used 
the  book  in  the  classroom  for  helpful  criticisms  and  sug- 
gestions regarding  its  revision.  In  particular,  I  wish  to 
acknowledge  my  obligations  to  Dr.  Edmund  H.  Hollands 
for  many  suggestions  and  much  valuable  assistance,  espe- 
cially in  the  collection  and  arrangement  of  the  examples. 
My  thanks  are  also  due  to  Dr.  Hollands  and  to  Mr.  C.  H. 
Williams  for  aid  in  proof-reading. 

J.   E.   C. 

Cornell  University, 
August,  1909. 


TABLE   OF   CONTENTS 

Introduction 

CHAPTER   I 
The  Standpoint  and  Problem  of  Logic 

PAGB 

§  I.  Definition  of  the  Subject I 

§  2.  Relation  to  Psychology 5 

§  3.  Logic  as  a  Science  and  an  Art       .......  9 

§  4.  The  Material  of  Logic 14 

CHAPTER   II 

Important  Stages  in  the  Development  of  Logic 

§  5.  Socrates  and  the  Concept 19 

§  6.  Aristotle  and  the  Syllogism 23 

§  7.  Bacon  and  the  Inductive  Method  ......  28 

§  8.  Logic  from  the  Evolutionary  Standpoint 32 

Part  I.  —  The  Syllogism 

CHAPTER  III 

The  Syllogism  and  its  Parts 

§  9.     The  Nature  of  the  Syllogism  .......       36 

§10.   The  Parts  of  the  Syllogism 39 

§11.   Perception,  Conception,  and  Judgment 44 

CHAPTER   IV 

The  Various  Kinds  of  Terms 

§  12.  Singular,  General,  and  Collective  Terms 49 

§  13.  Abstract  and  Concrete  Terms 51 

§  14.  Positive  and  Negative  Terms 55 

§  15.  Absolute  and  Relative  Terms 57 

§  16.  Extension  and  Intension  of  Terms 58 


xii  Table  of  Contents 


CHAPTER  V 

Definition  and  Division 

PAGE 

§17.    Fixing  the  Meaning  of  Terms 64 

§  18.    Definition 66 

§  19.   Division 77 

CHAPTER  VI 

Propositions 

§  20.  The  Nature  of  a  Proposition 84 

§21.  The  Quality  and  Quantity  of  Propositions 86 

§  22.  Difficulties  in  Classification    ........  89 

§  23.  Formal  Relation  of  Subject  and  Predicate 90 

CHAPTER   VII 

The  Interpretation  of  Propositions 

§  24.  The  So-called  Process  of  Immediate  Inference      ....  97 

§  25.  The  Opposition  of  Propositions 99 

§  26.  The  Obversion  of  Propositions 103 

§  27.  The  Conversion  of  Propositions 105 

§  28.  Contraposition  and  Inversion 108 

CHAPTER    VIII 

The  Syllogism 

§29.   The  Nature  of  Syllogistic  Reasoning 1 12 

§30.   The  Rules  of  the  Syllogism   .         .         , 115 

§31.  The  Figures  of  the  Syllogism 120 

CHAPTER   IX 

The  Valid  Moods  and  the  Reduction  of  Figures 

§  32.   The  Moods  of  the  Syllogism 122 

§33.   The  Special  Canons  of  the  Four  Figures 123 

§  34.   The  Determination  of  the  Valid  Moods  in  Each  of  the  Figures     .     127 

§  35.   The  Mnemonic  Lines I29 

CHAPTER   X 

Abbreviated  and  Irregular  Forms  of  Argument 

§  36.    Enthymemes •  *33 

§  37.    Prosyllogisms  and  Episyllogisms *34 


Table  of  Contents  xiii 

PAGE 

§  38.    Sorites,  or  Chains  of  Reasoning     .         .         .        •         •         .         .136 
§  39.    Irregular  Arguments 139 

CHAPTER   XI 

Hypothetical  and  Disjunctive  Arguments 

§  40.  The  Hypothetical  Syllogism  ........     I44 

§  41.  Relation  of  Categorical  and  Hypothetical  Arguments   .         .         .     148 

§  42.  Disjunctive  Arguments          .         .         .         .         .         .         .         .154 

§  43.   The  Dilemma 156 

CHAPTER   XII 

Fallacies  of  Deductive  Reasoning 

§  44.  Classification  of  Fallacies 164 

§  45.  Errors  in  Interpretation 166 

§  46.  Formal  Fallacies '.         .         •         .         .170 

§  47.  Material  Fallacies 171 


Part  II.  —  Inductive  Methods 

CHAPTER  XIII 

The  Problem  of  Induction 

§  48.   The  Problem  of  Induction 190 

§  49.   The  Enumeration  of  Instances 192 

§  50.   Induction  through  Analysis 196 

CHAPTER   XIV 

The  Assumptions  of  Induction  —  Stages  in  the  Inductive  Procedure 

§51.   The  Assumptions  of  Induction 202 

§  52.    Stages  in  the  Inductive  Process 205 

§  53.   Observation  and  Explanation 207 

CHAPTER   XV 

Enumeration  and  Statistics 

§  54.    Enumeration  or  Simple  Counting 216 

§  55.    Statistics  and  Statistical  Methods 220 

§  56.   The  Calculation  of  Chances  ........     228 


xiv  Table  of  Contents 

CHAPTER   XVI 

Determination  of  Causal  Relations 

PAG* 

§  57.   Causal  Connection 234 

§  58.    Mill's  Experimental  Methods 237 

§  59.   The  Method  of  Agreement 239 

§  60.   The  Method  of  Difference 244 


CHAPTER   XVII 

Determination  of  Causal  Relations  (continued) 

§61.   The  Joint  Method  of  Agreement  and  Difference   ....     249 

§  62.   The  Method  of  Concomitant  Variations 255 

§  63.   The  Method  of  Residues 260 

CHAPTER   XVIII 
Analogy 

§  64.    Explanation  by  Analogy 266 

§  65.    Analogy  as  Suggestive  of  Explanatory  Hypotheses        .         .         .     271 
§  66.   The  Incompleteness  of  Analogical  Reasoning       ....     274 

CHAPTER   XIX 

The  Use  of  Hypotheses 

§  67.  Reasoning  from  an  Hypothesis 278 

§  68.  Formation  of  Hypotheses 282 

§  69.  The  Proof  of  an  Hypothesis 285 

§  70.  Requirements  of  a  Good  Hypothesis 293 

CHAPTER   XX 

Fallacies  of  Induction 


§71.  The  Source  of  Fallacy 

§  72.  Fallacies  due  to  the  Careless  Use  of  Language 

§  73.  Errors  of  Observation    ..... 

§  74.  Mistakes  in  Reasoning 

§  75.  Fallacies  due  to  Individual  Prepossessions     . 


298 
299 
3°3 
309 
312 


Table  of  Contents  xv 

Part  III. — The  Nature  of  Thought 

CHAPTER   XXI 
Judgment  as  the  Elementary  Process  of  Thought 

PAGB 

§  76.  Thinking  the  Process  by  which  Knowledge  grows  or  develops      .  316 

§  77.  The  Law  of  Evolution  and  its  Application  to  Logic      .         .  317 

§  78.  Judgment  as  the  Starting-point 322 

§  79.  Concepts  and  Judgment 324 

CHAPTER   XXII 

The  Main  Characteristics  of  Judgment 

§80.  The  Universality  of  Judgments 329 

§81.  The  Necessity  of  Judgments 331 

§  82.  Judgment  involves  both  Analysis  and  Synthesis    ....  334 

§  83.  Judgment  as  constructing  a  System  of  Knowledge         .         .         .  339 

CHAPTER   XXIII 

The  Laws  of  Thought 

§  84.  The  Law  of  Identity 343 

§  85.   The  Law  of  Contradiction 350 

§  86.   The  Law  of  Excluded  Middle 352 

CHAPTER   XXIV 

Types  of  Judgment 

§  87.   Judgments  of  Quality 355 

§  88.    Judgments  of  Quantity 358 

§  89.   Judgments  of  Causal  Connection 362 

§  90.  Judgments  of  Individuality 370 

CHAPTER   XXV 

The  Nature  of  Inference.  —  Induction  and  Deduction 

§  91.   Judgment  and  Inference 373 

§  92.   The  Nature  of  Inference 378 

§  93.   Induction  and  Deduction 384 


xvi  Table  of  Contents 

CHAPTER   XXVI 
The  Unification  of  Knowledge 

PAGH 

§  94.   Science  and  Philosophy 390 

§  95.    Science  as  Philosophy 395 

§  96.   The  Assumptions  of  the  Sciences 399 

§  97.    Philosophy  as  the  Interpretation  of  the  Sciences  ....  405 

Questions  and  Exercises 409 

Miscellaneous  Exercises  in  Propositions 424 

Miscellaneous  Examples  of  Deductive  Arguments         .         .         .  435 

Miscellaneous  Examples  of  Inductive  Arguments           .         .         .  469 

Index .  517 


INTRODUCTION 

CHAPTER   I 

THE    STANDPOINT    AND    PROBLEM    OF    LOGIC 

§  i.  Definition  of  the  Subject.  — Logic  may  be  defined  as 
the  science  of  thought,  or  as  the  science  which  investigates 
the  process  of  thinking.  Every  one  knows,  in  a  general  way 
at  least,  what  is  meant  by  thinking,  and  has  noticed  more  or 
less  consciously  some  of  its  peculiarities.  Thinking  is  the 
intellectual  act  by  means  of  which  knowledge  is  obtained. 
We  do  not  really  know  any  fact  until  we  think  it;  that  is, 
until  the  mind  sets  it  in  its  proper  relation  to  the  other  parts  of 
its  experience,  and  thus  comes  to  understand  its  true  mean- 
ing. We  make  a  distinction,  for  example,  between  what  has 
come  to  us  through  report  or  hearsay,  and  conclusions  which 
we  have  reached  by  our  own  thinking.  '  I  have  heard,'  we 
say,  '  that  A  is  dishonest,  but  I  do  not  know  it.'  That  is, 
this  fact  has  not  been  reached  as  a  result  of  our  own  thinking, 
and  cannot  therefore  claim  the  title  of  knowledge.  On  the 
other  hand,  that  the  earth  is  round,  is  not  a  mere  matter  of 
hearsay  for  an  educated  man.  It  is  a  piece  of  knowledge, 
because  it  is  a  conclusion  which  he  has  reached  by  thinking, 
or  by  putting  together  various  facts  for  himself. 

Logic,  then,  is  the  science  which  treats  of  the  operations  of 
the  human  mind  in  its  search  for  truth.     Logic  must  always 

B  I 


2  The  Standpoint  and  Problem  of  Logic 

assume  that  the  thinking  which  it  investigates  has,  as  its 
aim  and  object,  the  attainment  of  truth.  Thinking  is  thus 
an  expression  of  the  will  as  well  as  of  the  intelligence.  Again, 
as  seeking  truth,  thinking  is  not  a  mere  arrangement  of  ideas 
in  our  heads,  but  is  a  dealing  with  the  nature  of  objects. 
Thought  cannot  exist  in  itself  or  by  itself  as  something  merely 
in  our  minds,  but  it  is  its  very  nature  to  refer  to  real  things, 
existing  in  an  objective  world.  This  follows  directly  from 
our  definition  of  thought  as  concerned  with  truth.  Truth 
is  no  private  state  of  the  subjective  mind,  but  something 
objective  that  is,  in  a  sense,  independent  of  the  individual 
thinker  and  his  ideas. 

In  denning  Logic  as  a  science,  we  mean  that  it  seeks  to 
substitute  exact  and  systematic  knowledge  regarding  the 
nature  of  thought  for  the  popular  notions  to  be  found  in 
everyday  life.  Like  all  the  sciences,  logic  has  to  correct 
and  supplement  ordinary  knowledge.  It  is  its  mission  to 
help  us  to  understand  more  exactly  and  completely  the  way 
in  which  thinking  goes  on,  and  to  enumerate  and  describe,  as 
fully  and  precisely  as  possible,  the  various  modes  and  types 
of  thought  which  are  employed  in  gaining  knowledge. 

But  it  is  also  the  business  of  a  science  to  systematize  facts. 
Logic,  then,  cannot  content  itself  with  a  mere  description  of 
this  or  that  kind  of  thinking,  in  isolation  from  other  ways 
in  which  we  think.  It  must  also  deal  with  the  way  in  which 
the  various  kinds  of  thinking  are  related.  For  example,  we 
apply  such  terms  as  '  conception,'  'judgment,'  '  induction,' 
and  'deduction'  to  different  intellectual  operations,  and  give 
the  distinguishing  characteristic  in  each  case.  But  it  is  neces- 
sary as  well  to  understand  how  these  processes  are  related. 
Since  all  thinking  has  one  end,  the  discovery  of  truth,  the 


§  I.    Definition  of  the  Subject  3 

various  intellectual  operations  must  mutually  cooperate  and 
assist  in  this  result.  All  of  the  logical  processes,  then,  stand 
in  relation  to  one  another.  They  are  all  parts  of  the  one  in- 
telligence, though  they  may  well  represent  different  stages  or 
steps  in  its  work  of  obtaining  knowledge.  It  is  therefore 
the  business  of  logic  to  show  us  the  organic  structure  of 
thought.  In  other  words,  Logic  must  furnish  a  compre- 
hensive view  of  the  way  in  which  intelligence  acts,  and  the 
part  which  processes  like  '  conception,'  '  judgment,'  '  induc- 
tion,' etc.,  play. 

(1)  The  word '  logic '  is  derived  from  the  adjective  corresponding 
to  the  Greek  noun  Aoyos,  which  signifies  either  a  complete  thought, 
or  a  word  as  the  expression  of  that  thought.  The  singular  form  of 
the  adjective  XoyiKrj,  from  which  the  English  word  is  derived,  was 
supposed  to  qualify  either  eVto-T^r;,  as  applying  to  the  theoretical 
science  of  logic,  or  re^vr],  as  referring  to  the  practical  application 
of  its  rules  and  as  affording  guidance  in  the  art  of  correct  reason- 
ing. We  shall  have  to  raise  the  question  in  a  subsequent  section 
how  far  it  is  possible  to  regard  logic  as  an  art,  or  a  system  of  rules 
which  teach  us  how  to  reason  correctly. 

The  use  of  the  same  term  (Aoyos)  by  the  Greeks  to  denote 
both'  thought,'  and '  word '  or '  discourse,'  emphasizes  the  close  and 
vital  relation  between  thought  and  its  expression  in  language. 
Whether  thinking  can  go  on  without  language  is  a  psychological 
question  that  we  cannot  here  decide.  But  it  is  certain  that  in 
adult  human  thinking  the  thought  and  its  verbal  expression  are 
inseparably  connected,  just  as  the  principle  of  life  is  connected  with 
the  functions  and  activities  of  the  physical  organism.  The  word 
is  no  arbitrary  or  external  mark  attached  to  a  ready-made  thought 
which  exists  independently.  The  verbal  expression  is  rather  the 
means  in  which  and  through  which  the  thought  completes  itself. 
It  is  that  which  gives  to  the  thought,  not  only  a  name,  but  an  abid- 


4  The  Standpoint  and  Problem  of  Logic 

ing  reality  as  a  permanent  possession.  To  introduce  a  new  term 
into  a  science  is  not  indeed  always  a  great  intellectual  achievement. 
New  names  may  be  coined  for  facts  and  conceptions  that  are 
already  familiar.  But,  on  the  other  hand,  new  thoughts  and  dis- 
coveries must  find  expression  either  in  the  employment  of  new 
terms,  or  in  the  use  of  old  terms  in  a  new  and  more  definite  sense. 
What  has  been  said  will  suffice  to  make  clear  the  close  relation 
between  Logic  and  Rhetoric.  Logic  finds  the  products  of  think- 
ing expressed  in  language,  and  to  a  considerable  extent  may  be  said 
to  be  concerned  with  the  meaning  of  words,  sentences,  and  spoken 
or  written  arguments.  It  is  impossible  to  make  any  sharp  divi- 
sion between  the  thoughts  and  their  relations,  on  the  one  hand,  and 
the  form  of  the  words  and  sentences  with  which  rhetoric  concerns 
itself,  on  the  other.  We  may  say,  then,  that  definiteness  of  thought 
is  a  condition  of  clearness  and  accuracy  in  the  use  of  language,  and 
also  that  the  effort  to  express  oneself  with  clearness  and  pre- 
cision demands  and  involves  logical  pains  and  exactness.  Indeed, 
clear  thinking  and  accurate  verbal  expression  are  one  and  in- 
separable, as  are  also  careless  or  indolent  ways  of  thinking  and  slip- 
shod and  slovenly  use  of  language.  By  taking  the  trouble  to  ex- 
press oneself  with  precision  one  forms  the  habit  of  thinking  rightly. 
(2)  We  have  defined  logic  as  the  science  of  the  operations  and 
processes  of  thought,  or  as  the  science  of  thinking.  It  is  evident, 
however,  that  this  definition  does  not  carry  us  very  far  unless  we 
know  what  thinking  means.  And  to  gain  a  clearer  idea  of  this  com- 
mon term  may  be  said  to  be  the  problem  of  logic.  This  is,  however, 
by  no  means  as  easy  a  task  as  may  at  first  appear.  Familiar  words 
and  phrases  often  conceal  difficulties.  They  are  constantly  repeated 
without  reflection,  and  this  very  frequency  of  repetition  is  likely 
to  prevent  us  from  trying  to  gain  any  clear  ideas  regarding  the 
nature  of  the  objects  which  they  denote.  It  is  only  when  we 
become  discontented  with  our  knowledge  regarding  any  subject, 
when  doubts  arise  whether  we  really  understand  the  meaning  of 


§  2.    Relation  to  Psychology  5 

the  words  which  we  use,  that  we  attempt  to  make  our  knowledge 
scientific,  i.e.,  to  gain  clear,  definite,  and  systematic  ideas.  This 
can  perhaps  be  made  clearer  by  considering  the  main  differences 
between  an  educated  and  an  uneducated  man.  The  educated  man 
has,  of  course,  a  great  deal  more  information  than  the  other,  and 
his  knowledge  is  more  definite  and  systematic.  But  a  second  and 
more  important  distinction  is  found  in  the  attitude  of  mind  which 
education  begets.  The  educated  man  is  desirous  of  knowing  more, 
because  he  is  sensible  of  his  own  ignorance.  The  uneducated 
man,  on  the  other  hand,  supposes  that  he  knows  all  about  things 
whose  names  are  familiar  to  him.  He  can  settle  puzzling  theo- 
logical or  political  problems  off-hand  in  a  way  which  is  perfectly 
satisfactory  to  himself,  without  study,  and  almost  without  reflec- 
tion. 

§  2.  Relation  to  Psychology.  —  It  may  aid  us  in  obtain- 
ing a  clearer  view  of  what  thinking  is,  if  we  compare  the 
general  standpoint  of  logic  with  that  of  psychology.  Both 
of  these  sciences  deal  with  what  goes  on  in  mind  or  con- 
sciousness, and  are  thus  opposed  to  the  so-called  objective 
sciences,  which  are  all  concerned  with  some  group  or  field 
of  external  facts.  But,  in  spite  of  this  agreement,  there 
is  an  important  distinction  between  logic  and  psychology. 
In  the  first  place,  psychology  deals  with  all  that  there  is 
in  mind.  It  describes  pleasures  and  pains,  acts  of  will, 
and  the  association  of  ideas,  as  well  as  what  is  usually  called 
logical  thinking.  But  logic  does  not  differ  from  psychol- 
ogy simply  by  being  less  inclusive  than  the  latter.  I*  is 
true  that,  from  the  standpoint  of  psychology,  the  thought- 
process  is  merely  a  part  of  the  mental  content,  which  has 
to  be  analyzed  and  described  like  anything  else  which 
goes    on    in    consciousness.    Thinking    has    doubtless    for 


6  The  Standpoint  and  Problem  of  Logic 

psychology  peculiar  marks  or  characteristics  which  dis 
tinguish  it  from  other  related  processes  like  those  of  asso- 
ciation ;  but  when  these  have  been  found,  and  the  psycho- 
logical description  of  thinking  is  complete,  the  question 
with  which  logic  deals  has  not  yet  been  raised.  For  logic, 
as  we  shall  see  presently,  adopts  a  different  standpoint, 
and  investigates  with  a  different  end  in  view. 

The  important  difference  is  this:  In  psychology  we  are 
interested  in  the  content  of  consciousness  for  its  own  sake, 
and  just  as  it  stands.  We  try  to  find  out  what  actually 
goes  on  in  our  minds,  and  to  describe  it  just  as  we  should 
any  event  which  occurs  in  the  external  world.  But  in  logic 
the  question  is  not:  What  are  mental  processes?  but  rather: 
What  knowledge  do  they  give  us,  and  is  this  knowledge 
true  or  false?  Logic,  in  other  words,  does  not  regard  the 
way  in  which  ideas  exist,  and  is  not  interested  in  them  for 
what  they  are,  but  rather  in  the  purpose  which  they  sub- 
serve in  affording  us  knowledge  of  something  beyond  them- 
selves. Psychology,  in  its  description  of  conscious  states, 
inquires  regarding  their  quality,  intensity,  duration,  etc., 
and  the  ways  in  which  they  combine  with  each  other  to 
form  complex  ideas.  The  problem  with  which  logic  is 
concerned,  on  the  other  hand,  has  reference  to  the  value 
of  ideas  when  they  are  taken  to  represent  facts  in  the  real 
world.  As  we  have  already  seen,  thinking  is  the  pursuit 
of  truth ;  and,  in  dealing  with  thoughts,  logic  has  to  describe 
and  evaluate  them  in  relation  to  this  end.  Hence  for  logic 
thoughts  are  true  or  false,  i.e.,  they  are  in  harmony 
or  not  in  harmony  with  truth,  which  is  the  standard  or 
norm  that  thought  sets  up  as  its  purpose  or  end.  Psychol- 
ogy, on  the  other  hand,  does  not  ask  ?t  all  whether  the 


§  2.    Relation  to  Psychology  7 

ideas  are  true  or  false,  good  or  bad.  It  does  not  seek  to 
evaluate  ideas  in  the  light  of  some  standard,  but  confines 
itself  to  describing  their  actual  mode  of  existence. 

Consider  a  little  further  the  nature  of  the  ideas  with  which 
logic  deals.  Every  idea,  as  we  have  seen,  not  only  exists 
in  some  definite  fashion  in  some  particular  consciousness, 
connected  with  certain  other  ideas,  and  with  a  definite 
quality,  intensity,  etc.,  but  it  has  a  meaning  or  significance 
as  a  piece  of  knowledge.  It  not  only  is  something,  but 
it  also  stands  for  or  signifies  something.  Now  it  is  not 
with  the  existence,  but  with  the  meaning  side  of  ideas  that 
logic  has  to  do.  A  logical  idea,  or  piece  of  knowledge, 
is  not  merely  a  modification  of  consciousness  which  exists 
in  the  mind  of  some  individual  at  a  particular  time.  For 
example,  the  proposition:  '  The  three  angles  of  a  triangle  are 
equal  to  two  right  angles,'  will  give  rise  to  a  number  of 
definite  psychological  processes  (probably  auditory  or 
visual  in  character)  in  the  mind  of  any  individual.  These 
processes  would  also  probably  differ  in  character  in  the 
case  of  two  persons.  The  meaning  of  the  proposition, 
however,  is  distinct  from  the  definite  processes  which  arise 
in  particular  minds.  The  proposition  has  a  significance 
as  an  objective  fact,  or  piece  of  knowledge,  outside  my 
individual  mind;  the  psychological  images  or  processes  may 
differ  for  different  persons,  but  the  fact  expressed  is  the 
same  for  all  minds  and  at  all  times. 

(1)  The  relation  between  logic  and  psychology  may  perhaps  be 
illustrated  by  referring  to  that  which  exists  between  morphology 
and  physiology.  Morphology  deals  with  the  form  and  structure 
of  living  organisms,  and  physiology  with  the  various  acts  and  func- 
tions which  these  organisms  discharge  in  fulfilling  the  ends  of  life. 


8  The  Standpoint  and  Problem  of  Logic 

Thus  we  speak  of  the  former  as  the  science  of  form  or  structure, 
and  of  the  latter  as  the  science  of  function.  In  the  same  way, 
psychology  may  be  said  to  deal  with  the  actual  structure  of  mental 
processes,  and  logic  with  the  part  which  they  play  in  giving  us 
knowledge. 

It  must  be  noticed,  however,  that  this  is  a  distinction  made  for 
purposes  of  investigation,  and  does  not  denote  that  structure  and 
function  have  nothing  to  do  with  each  other.  On  the  contrary, 
some  knowledge  of  the  function  is  often  necessary  in  order  to  under- 
stand the  structure  of  an  organ;  and,  on  the  other  hand,  it  is  usually 
true  that  the  nature  of  a  function  only  becomes  completely  intelligi- 
ble when  the  character  of  the  mechanism  with  which  it  works  is 
known.  And  the  same  holds  true,  I  think,  of  the  relations  between 
psychology  and  logic.  Although  it  has  been  found  profitable  when 
dealing  with  consciousness,  as  in  the  biological  realm,  to  investigate 
the  nature  of  structure  and  function  separately,  yet  here,  as  there, 
the  two  lines  of  inquiry  cross  each  other;  for  it  is  beyond  question 
that  the  knowledge  we  obtain  by  thinking  is  largely  dependent  upon 
the  character  (quality,  intensity,  etc.)  of  the  actual  processes  in  con- 
sciousness. To  understand  the  nature  of  a  logical  idea,  then,  it  is 
often  necessary  to  refer  to  the  psychological  facts  and  their  actual 
mode  of  behaviour.  And  it  is  equally  true  that  one  cannot  carry 
on  a  psychological  investigation  into  the  nature  of  mental  processes 
without  taking  account,  to  some  extent,  of  the  part  which  they  play 
in  giving  us  knowledge.  No  psychology  is  able  to  take  ideas  simply 
as  existing  conscious  processes  to  which  no  further  meaning  or 
importance  attaches;  it  is  only  with  reference  to  the  function  they 
perform  as  knowing  states  that  their  own  peculiar  character  can  be 
understood.  In  other  words,  the  intellectual  activities  and  purposes 
of  mind  must  be  presupposed  in  psychology,  though  this  science,  for 
the  most  part,  goes  its  way  as  if  the  ideas  were  not  cognitive  at  all. 
At  least  this  seems  to  be  true  of  the  'new'  or  experimental  psy- 
chology, as  opposed  to  the  older  philosophies  of  mind. 


§  3-    Logic  as  a  Science  and  an  Art  9 

(2)  It  would  of  course  be  presumptuous,  as  well  as  utterly  useless, 
for  any  writer  to  draw  a  hard  and  fast  line  between  logic  and  psy- 
chology, and  to  forbid  others  to  overstep  it.  In  attempting  to  dis- 
cover the  dividing  line  between  two  closely  related  sciences,  one 
must  be  guided  by  the  procedure  of  those  who  are  working  in  the 
fields  which  it  is  proposed  to  divide.  Now,  it  must  be  admitted  that 
by  no  means  all  of  the  recent  writers  in  psychology  limit  the  sphere 
of  their  science  in  the  way  above  described;  that  is,  there  are 
certain  psychologists  who  do  not  confine  their  attention  to  the  mere 
mental  processes  as  such,  but  include  in  their  investigations  the  fur- 
ther problem  regarding  the  function  which  these  processes  play  in 
giving  us  knowledge.  Thus  in  Professor  James's  Principles  oj 
Psychology  there  is  an  excellent  chapter  on  '  Reasoning,'  which  cer- 
tainly contains  as  much  logical  as  psychological  matter.  In  gen- 
eral, one  may  say  that  at  the  present  time  psychologists  are  tending 
to  deal  with  mind  more  from  a '  functional '  than  a '  structural '  point 
of  view.  That  is,  the  tendency  is  now  to  emphasize  the  activities  of 
conscious  life,  and  thus  to  interpret  mind  in  the  light  of  the 
results  it  achieves,  rather  than  to  explain  it  solely  in  terms  of  the 
elements  of  which  it  is  composed.  But  this  functional  psychology 
is  not  identical  with  logic.  For,  in  the  first  place,  it  does  not  limit 
itself,  as  the  latter  does,  to  the  cognitive  functions  of  mind.  And, 
secondly,  it  tends  to  interpret  even  ideas  and  judgments  in  their 
relation  to  the  life  of  the  psychophysical  organism  in  general, 
rather  than  as  elements  in  the  life  of  reason  or  truth.  It  is  only 
logic  which  looks  at  mental  life  definitely  and  exclusively  from  this 
point  of  view.  For  logic,  the  thinking  process  is  not  a  mere  aspect 
of  living,  but  something  to  be  investigated  and  understood  solely 
in  its  relation  to  truth,  or  the  rational  consistency  which  is  its 
end  and  goal. 

§  3.  Logic  as  a  Science  and  an  Art.  — We  have  defined 
logic  as  the  science  of  thought,  but  it  has  often  been  pointed 


10  The  Standpoint  and  Problem  of  Logic 

out  that  there  are  equally  strong  reasons  for  considering 
it  to  be  an  art.  The  purpose  of  logical  study,  it  is  often 
said,  is  to  help  us  to  think  correctly,  to  prevent  us  from 
falling  into  errors  in  our  own  reasoning,  and  from  being 
misled  by  the  fallacious  arguments  of  others.  The  difference 
between  a  science  and  an  art  in  general  is  that  a  science  is 
interested  in  the  discovery  of  facts  and  laws  without  any 
thought  of  what  use  may  be  made  of  this  knowledge ;  an  art, 
on  the  contrary,  gives  practical  guidance  and  direction  for 
some  course  of  action.  The  question  before  us,  then,  is 
this:  Does  logic  merely  give  us  knowledge  about  the  ways 
in  which  we  think,  or  does  it  also  help  us  to  think  rightly? 

Before  we  attempt  to  answrer  this  question,  we  must 
note  that  practical  rules  of  action  are  based  upon  scientific 
knowledge.  An  art,  in  other  words,  depends  upon  science, 
and  grows  in  perfection  with  the  advance  of  scientific  know- 
ledge. Thus  medicine,  as  the  art  of  healing,  is  founded 
upon  the  sciences  of  chemistry,  physiology,  and  anatomy, 
and  it  is  because  of  the  great  discoveries  which  have  been 
made  in  these  fields  within  recent  years  that  it  has  been 
able  to  advance  with  such  gigantic  strides.  Again,  the 
art  of  singing,  in  so  far  as  it  is  an  art  which  can  be  taught 
and  learned,  depends  upon  a  knowledge  of  the  physical 
and  physiological  laws  of  the  vocal  organs.  An  art,  then, 
always  presupposes  a  certain  amount  of  science,  or  know- 
ledge, and  is  simply  the  application  of  this  knowledge  to 
some  practical  purpose.  In  some  cases,  the  application  is 
very  obvious  and  direct;  in  others,  it  is  much  more  difficult 
to  determine;  but,  in  general,  there  is  always  this  relation 
between  theory  and  practice,  between  knowledge  and  action. 

From  what  has  been  already  said,  it  will  be  evident  that 


§  3-    Logic  as  a  Science  and  an  Art  n 

logic  must  first  be  a  science  before  it  can  become  an  art. 
Its  first  business  must  be  to  investigate  the  nature  of  thought, 
and  to  attempt  to  discover  the  different  forms  which  the 
latter  assumes  in  its  work  of  attaining  knowledge.  So 
that  we  were  right  in  defining  it  as  primarily  a  science. 
But  the  further  question  remains:  How  far  is  it  possible 
to  apply  the  laws  of  logic,  after  they  have  been  discovered, 
in  such  a  way  as  to  obtain  directions  for  reasoning  correctly 
in  every  case?  Can  we  not  apply  our  knowledge  of  the 
laws  of  thought  in  such  a  way  as  to  get  a  complete  art  of 
reasoning,  just  as  the  laws  of  chemistry  and  biology  are 
applied  in  medicine? 

It  is  no  doubt  true  in  logic,  as  everywhere,  that  scien- 
tific knowledge  is  capable  of  practical  application.  But 
I  do  not  think  that  logic  can  be  regarded  as  an  art,  in  the 
sense  that  it  furnishes  a  definite  set  of  rules  for  thinking 
correctly.  There  is  an  important  distinction  in  this  case 
which  must  not  be  left  out  of  account.  The  physical, 
and  even  the  biological  sciences,  deal  with  things  whose 
way  of  acting  is  perfectly  definite  and  uniform.  The  char- 
acter of  any  of  the  physiological  functions,  as,  e.g.,  digestion, 
may  be  comparatively  complex  and  difficult  to  determine, 
but  it  normally  attains  its  end  through  the  use  of  the  same 
means.  When  once  its  laws  are  understood,  it  is  not  dif- 
ficult to  prescribe  just  how  the  proper  means  may  always 
be  secured  for  the  attainment  of  the  desired  end.  But 
thinking  has  much  more  flexibility  in  its  way  of  acting. 
We  cannot  say  with  the  same  definiteness,  as  in  the  cases 
we  have  been  considering,  that  in  order  to  reach  a  certain 
end  we  must  use  a  definite  set  of  means.  It  is  not  possible, 
that  is,  to  say:   If  you  would  learn  what  is  true  about  any 


12  The  Standpoint  and  Problem  of  Logic 

particular  subject,  you  must  follow  this  rule  and  that  in  youi 
thinking.  Logic,  it  seems  to  me,  cannot  be  regarded  as  an 
art  like  photography,  or  even  like  medicine;  for  it  is  not 
possible  to  lay  down  definite  rules  for  the  guidance  of  think- 
ing in  every  case.  What  we  can  do,  is  to  show  the  method 
by  which  new  truths  have  been  discovered,  and  the  gen- 
eral conditions  which  must  always  be  fulfilled  in  reasoning 
correctly.  And  it  is  also  possible  to  point  out  the  more  com- 
mon errors  which  arise  when  these  conditions  are  violated. 
But  it  is  beyond  the  power  of  logic  to  formulate  any  definite 
set  of  rules  for  the  guidance  of  thinking  that  can  be  learned 
and  applied  as  a  prescription  for  every  case  ;  and  students 
whose  only  interest  in  the  subject  is  the  practical  one  of 
finding  some  rules  that  may  be  directly  applied  to  make 
them  infallible  reasoners  are  likely  to  be  disappointed. 

The  necessity  of  devoting  oneself  to  a  science  quite  unself- 
ishly cannot  be  too  strongly  enjoined,  nor  the  evils  which 
arise  when  one  begins  a  study  '  greedy  for  quick  returns  of 
profit,'  too  often  emphasized.  Nevertheless,  since  the  question 
has  been  raised,  it  would  not  be  just  to  refuse  altogether 
to  speak  of  the  practical  results  arising  from  a  study  of 
logic.  As  we  have  seen,  we  cannot  hope  to  become  infallible 
reasoners  by  its  aid.  It  is  just  as  true  here  as  in  any  other 
field,  however,  that  knowledge  is  power,  and  ignorance 
synonymous  with  weakness.  For  even  if  one  resolves 
never  to  look  inside  a  logic  book,  one  must  nevertheless 
have  some  theory,  or  act  upon  some  principle  —  it  may 
be  quite  unconsciously  —  in  deciding  what  is  true  and 
what  is  false.  For  instance,  a  man  may  act  upon  the  prin- 
ciple that  those  things  are  likely  to  be  true  which  are  favour- 
able to  his  own  interests,  or  which  agree  with  his  own  preju- 


§  3-    Logic  as  a  Science  and  an  Art  13 

dices,  or  with  the  articles  of  his  church  or  political  party. 
Or  again,  he  may  regard  his  senses  as  the  standards  of 
truth.  Mr.  Bradley  says  that  if  dogs  reason,,  they  proceed 
upon  the  principle,  '  what  smells,  exists,  and  what  docs 
not  smell  does  not  exist.'  It  is  not  uncommon  to  hear 
it  announced:  What  can  be  perceived  through  the  senses 
is  true;  what  cannot  be  sensed,  or  is  contrary  to  the 
testimony  of  the  senses,  is  an  absurdity.  This  was  the 
standard  of  truth  adopted,  for  example,  by  those  who 
attempted  to  overthrow  the  Copernican  theory  by  declar- 
ing it  to  be  in  plain  contradiction  to  the  testimony  of  the 
senses. 

It  seems  evident,  therefore,  that  intellectual  beings  cannot 
escape  some  kind  of  logical  theory,  whether  they  hold 
it  consciously  or  unconsciously.  It  is  clear,  too,  that  the 
character  of  this  theory  will  determine  to  a  great  extent 
their  thoughts  and  opinions.  The  only  question  which 
remains  is  whether  it  is  better  to  leave  this  matter  entirely 
to  chance,  or  to  attempt  to  gain  some  clear  ideas  regarding 
the  nature  of  thinking,  and  the  conditions  under  which 
knowledge  arises.  It  can  scarcely  be  doubted  that,  even 
from  a  practical  point  of  view,  a  true  theory  is  better  than 
a  false  one.  A  man  who  has  reflected  upon  the  nature  of 
proof,  and  the  principles  of  reasoning,  is  much  less  likely 
to  be  deceived  than  one  who  is  guided  unconsciously  by 
assumptions  which  he  has  never  examined.  It  is  always  an 
advantage  to  know  exactly  the  nature  of  the  result  at  which 
we  are  aiming,  and  to  be  perfectly  clear  as  to  our  own  pur- 
poses. And  this  is  just  what  a  study  of  logic  aids  us  in 
attaining.  It  helps  us  to  understand  the  structure  of  know- 
ledge and  the  conditions  of  proof.    Moreover,  it  engenders 


14  The  Standpoint  and  Problem  of  Logic 

the  habit  of  criticising  propositions,  and  examining  the 
evidence  upon  which  they  rest.  Further,  the  importance 
of  this  study  for  a  theory  of  education  may  well  be  em- 
phasized. For  education,  at  least  in  so  far  as  it  undertakes 
to  train  the  knowing  powers  of  the  individual,  must  be 
based  upon  a  knowledge  of  the  necessary  laws  of  intelligence, 
and  of  the  steps  or  stages  which  it  passes  through  in  its 
process  of  development. 

§  4.  The  Material  of  Logic.  —  The  business  of  logic, 
as  we  have  seen,  is  to  discover  the  laws  of  thought  and  to 
show  the  differences  which  exist  between  real  and  imaginary 
knowledge.  Where  now  shall  we  find  the  materials  for 
this  study  ?  Where  are  the  facts  which  are  to  be  taken 
as  a  starting-point?  It  is,  of  course,  impossible  to  learn 
directly  from  one's  own  consciousness  all  that  thinking 
is,  or  everything  of  which  it  is  capable.  For,  quite  apart 
from  the  difficulty  of  observing  the  process  of  thought 
while  it  is  actually  going  on,  no  one  can  suppose  that  his 
own  mind  furnishes  an  example  of  all  that  thinking  has 
done,  or  can  do.  It  is  necessary  to  take  a  broader  view, 
and  learn  how  other  men  think.  Of  course,  we  cannot 
look  into  the  consciousness  of  other  men,  but  we  can  study 
the  products  and  results  of  their  thoughts.  The  history 
of  the  way  in  which  truth  has  been  discovered  is  of  the 
greatest  importance  for  logic.  We  have  already  spoken 
of  thinking  as  having  truth  as  its  standard  or  norm.  It 
is  for  this  reason  that  logic  is  sometimes  called  a  normative 
science,  since  like  ethics  and  aesthetics  it  looks  at  the  expe- 
rience it  studies  as  realizing  an  end.  But  where  does  logic 
find  its  norm  ?  It  has  no  a  priori  method  of  deciding  what 
is  true  and  what  is  false,  what  is  knowledge  and  what  is 


§  4-    The  Material  of  Logic  15 

not.  But  in  the  various  sciences  of  nature  and  of  man, 
we  have  a  body  of  accepted  truth  that  has  been  verified 
by  the  experience  of  a  great  many  individuals.  Now,  it 
is  to  this  we  must  look  if  we  would  know  what  knowledge 
is,  and  it  is  in  the  processes  through  which  it  has  been  built 
up  that  we  find  the  norm  of  correct  thinking.  The  history 
of  the  various  sciences  furnishes  a  record  of  the  steps  by 
means  of  which  thought  has  built  up  knowledge.  And, 
in  this  record,  we  have  also  a  revelation  of  the  nature  of 
the  thinking  process  itself,  and  of  the  stages  through  which 
it  has  passed  in  the  course  of  its  development. 

It  is  by  a  reflection,  then,  upon  the  nature  of  proposi- 
tions which  are  universally  regarded  as  true  that  the  laws 
of  logic  are  obtained.  There  is  always  a  permanent  body 
of  knowledge  which  no  one  thinks  of  calling  in  question. 
Both  in  everyday  knowledge,  and  in  the  sciences,  there 
are  a  great  number  of  propositions  which  are  found  true 
by  everybody  who  takes  the  trouble  to  verify  them.  And 
it  is  here  that  logic  finds  its  material.  Taking  the  facts 
and  propositions  which  are  recognized  as  certain  by  every 
one,  logic  examines  their  structure  in  order  to  learn  about 
the  nature  of  the  intellectual  processes  by  which  they  have 
been  discovered.  What  principles,  it  asks,  are  involved 
in  these  bodies  of  knowledge,  and  what  particular  acts  of 
thought  were  necessary  to  discover  them  ?  It  is  only  by 
examining  various  pieces  of  knowledge  in  this  way,  and 
attempting  to  trace  out  the  conditions  of  their  discovery, 
that  one  can  learn  anything  new  regarding  the  laws 
and  character  of  thought.  The  best  way  of  getting  in- 
formation about  what  thought  can  do,  is  to  study  what  it 
has  already  accomplished.      In   other  words,   there   is   no 


1 6  The  Standpoint  and  Problem  oj  Logic 

way  of  learning  about  thinking  except  by  studying  wha\ 
it  has  done. 

Every  piece  of  knowledge,  as  the  product  of  thinking,  is  to  some 
extent  a  revelation  of  the  nature  of  intelligence.  But  scientific 
knowledge  —  by  this  I  mean  the  results  of  the  philosophical  and 
historical  sciences  as  well  as  of  the  so-called  natural  sciences  — 
exhibits  perhaps  most  clearly  the  nature  of  thought.  For  the 
history  of  these  sciences  enables  us  to  see  the  process  of  know- 
ledge, as  it  were,  in  the  making.  In  tracing  the  history  of  philo- 
sophical and  scientific  ideas,  we  are  at  the  same  time  following 
the  laws  of  the  development  of  thought.  It  is  this  fact  which 
makes  the  history  of  philosophy  and  of  the  various  sciences  so 
instructive.  It  was  with  this  object  in  view,  to  take  but  a  single 
example,  that  Whewell  wrote  his  famous  History  of  the  Inductive 
Sciences.  He  was  interested,  that  is,  not  so  much  in  the  mere  facts 
and  names  with  which  he  dealt,  as  in  showing  the  nature  of  thinking 
and  the  methods  which  had  been  employed  in  gaining  a  knowledge 
of  the  world.  This  is  made  very  clear  in  the  introduction  to  another 
work  of  Whewell  from  which  I  quote:  "We  may  best  hope  to 
understand  the  nature  and  conditions  of  real  knowledge  by  studying 
the  nature  and  conditions  of  the  most  certain  knowledge  which  we 
possess ;  and  we  are  most  likely  to  learn  the  best  methods  of  discov- 
ering truth  by  examining  how  truths,  now  universally  recognized, 
have  really  been  discovered.  Now  there  do  exist  among  us  doc- 
trines of  solid  and  acknowledged  merit  certainly,  and  truths  of  which 
the  discovery  has  been  received  with  universal  applause.  These 
constitute  what  we  commonly  term  sciences ;  and  of  these  bodies  of 
exact  and  enduring  knowledge  we  have  within  our  reach  so  large  a 
collection  that  we  may  hope  to  examine  them  and  the  history  of 
their  formation  with  a  good  prospect  of  deriving  from  the  study  such 
instruction  as  we  need  seek."  l 

1  Whewell,  History  of  Scientific  Ideas,  3d  ed.,  Vol.  L,  p.  4. 


§  4.    The  Material  of  Logic  17 

We  have  been  insisting  that  the  materials  for  the  study 
of  logic  are  to  be  found  mainly  in  the  records  which  we 
possess  of  what  thinking  has  actually  accomplished.  Our 
own  consciousness,  it  was  said,  can  supply  but  a  very 
small  quantity  of  material.  To  learn  what  thinking  is, 
one  must  have  as  broad  a  survey  as  possible  of  its  achieve- 
ments. 

But  there  is  another  side  to  the  matter.  It  must  never 
be  forgotten  that  it  is  the  actual  operations  of  thought  with 
which  logic  is  concerned.  The  words  and  propositions 
which  express  the  results  of  thinking  must  never  be  allowed 
to  take  the  place  of  the  thoughts  themselves.  Now,  we 
cannot  directly  study  the  thoughts  of  any  other  individual. 
It  is  only  in  so  far  as  we  interpret,  through  our  own  con- 
sciousness, the  records  of  what  thinking  has  done,  that 
these  records  are  able  to  throw  any  light  upon  the  problem 
of  logic.  So  in  this  study,  as  elsewhere,  we  must  find  the 
key  to  the  material  in  our  own  consciousness.  If  we  are 
to  gain  any  real  ideas  of  the  character  of  the  thinking  pro- 
cesses by  means  of  which  the  sciences  have  been  built  up, 
we  must  reproduce  these  in  our  own  minds.  One's  own 
consciousness  must,  after  all,  furnish  the  key  which  makes 
intelligible  the  account  of  the  various  steps  which  the  thought 
of  mankind  has  taken  in  building  up  science  or  knowledge. 
The  materials  of  logic  which  history  furnishes  become  sig- 
nificant only  when  translated  into  acts  and  operations  which 
may  be  observed  in  our  own  minds. 


10-51 


1 8  The  Standpoint  and  Problem  of  Logic 

REFERENCES 

The  following  references  may  be  given  in  connection  with  §§  i  and 
2: — 

C.  Sigwart,  Logic,  Vol.  I.,  General  Introduction. 
F.  H.  Bradley,  The  Principles  of  Logic,  pp.  1-10. 
B.  Bosanquet,  Logic,  Vol.  I.,  Introduction. 

H.  L.  Mansel,  Prolegomena  Logica,  Chap.  I. 

R.  Adamson,  The  first  part  of  the  article  'Logic'  in  the  Encyclo- 
pedia Britannica. 

D.  G.  Ritchie,  The  Relation  of  Logic  to  Psychology,  Philos.  Review, 
Vol.  V.,  pp.  585-600;  Vol.  VI.,  pp.  1-17. 


CHAPTER  II 

IMPORTANT  STAGES  IN  THE  DEVELOPMENT  OF  LOGIC 

§  5.  Socrates  and  the  Concept.  —  Logic  was  founded 
as  a  separate  and  independent  branch  of  inquiry  by  Aris- 
totle (387-322  B.C.).  Almost  from  the  first  beginning 
of  philosophical  speculation,  —  which  took  its  rise  in  the 
sixth  century  in  the  Greek  cities  on  the  coast  of  Asia 
Minor,  and  in  Sicily  and  southern  Italy,  —  questions  had, 
however,  been  raised  regarding  the  nature  of  knowledge  and 
the  proper  value  to  be  assigned  to  different  forms  of  expe- 
rience. More  particularly,  these  early  thinkers  emphasized 
the  distinction  between  the  knowledge  given  by  sense-per- 
ception and  that  obtained  by  thinking  or  reasoning.  The 
latter  kind  of  knowledge,  it  was  generally  agreed,  is  alone 
trustworthy  and  genuine;  while  the  senses,  on  the  other 
hand,  are  bad  witnesses  and  do  not  show  us  the  true  nature 
of  things.  In  these  early  schools,  however,  logical  ques- 
tions about  truth  and  knowledge  were  largely  incidental, 
the  fundamental  interest  being  to  explain  the  nature  of 
the  physical  universe.  It  was  not  until  after  the  Persian 
wars,  when  Athens  had  become  the  intellectual  and  com- 
mercial centre  of  Greece,  that  the  inner  world  of  human 
experience  —  man's  knowledge,  moral  beliefs,  and  prac- 
tices, customs,  laws,  and  religions  —  came  to  be  of  primary 
interest  and  importance  to  philosophical  inquirers. 

19 


20      important  Stages  in  the  Development  of  Logic 

The  political  prominence  and  wealth  that  came  to  Athem 
as  a  result  of  her  leadership  in  the  wars  with  Persia,  led 
to  the  rapid  transformation  of  the  outward  appearance  of 
the  city  and  also  of  the  life  and  thought  of  its  inhabitants. 
The  new  times  and  the  wider  circle  of  political  and  social 
activities  which  were  thus  opened  up  to  citizens  of  Athens, 
demanded  that  the  older  system  of  education  —  the  tra- 
ditional music  and  gymnastic  —  should  be  supplemented 
by  some  more  advanced  instruction.  And,  in  response 
to  this  demand,  there  arose  a  class  of  teachers  called  So- 
phists, who  made  it  their  business  to  instruct  young  men  in 
all  the  practical  affairs  of  life,  and  especially  in  the  use  of 
words  and  the  art  of  public  speaking,  or  rhetoric,  as  it  was 
called.  The  Sophists  do  not  seem  to  have  made  it  their  ob- 
ject to  teach  truth  to  their  pupils,  or  to  inculcate  in  them  a 
love  and  reverence  for  truth;  they  sought  rather  to  make 
those  whom  they  taught  clever  men  of  the  world.  In  teach- 
ing the  art  of  argumentation  or  public  speaking  they  did 
not  confine  themselves  to  pointing  out  the  methods  by  which 
true  conclusions  could  be  reached,  but  went  on  to  teach  the 
arts  by  which  the  judges  could  be  persuaded,  and  tricks 
for  the  discomfiture  of  one's  adversary.  The  rhetoric  of 
the  Sophists,  in  other  words,  was  not  a  science  of  reasoning, 
but  an  art  of  persuasion  and  of  controversy.  It  was  not 
essential  to  have  any  real  knowledge  of  the  subject  under 
discussion  in  order  to  argue  well,  from  their  point  of  view, 
but  only  to  be  well  versed  in  all  the  arts  of  persuasion,  and 
quick  to  take  advantage  of  an  opponent's  errors. 

The  theory  on  which  the  teaching  of  the  Sophists  was 
based  is  usually  known  as  scepticism.  The  Sophists,  that 
is,  had  come  to  the  conclusion  that  it  is  impossible  to  find 


§  5-    Socrates  and  the  Concept  21 

any  fixed  standard  of  truth.  Looking  at  the  diversity 
of  individual  opinions  and  of  individual  feelings,  they 
declared  that  knowledge  or  truth  as  something  objective, 
or  the  same  for  all,  is  an  illusion.  Only  individual  opin- 
ions exist;  there  is  no  standard  by  reference  to  which  these 
opinions  may  be  measured.  Indeed,  the  words  '  truth ' 
and  'falsehood'  can  have  only  a  practical  meaning;  each 
individual  must  be  the  measure  of  truth  for  himself.  They 
lacked  the  scientific  spirit  that  aims  at  truth  which  is  objec- 
tive and  real;  like  men  everywhere  whose  interest  is  ex- 
clusively practical,  they  thought  truth  in  this  sense  abstract 
and  unmeaning,  and  aimed  only  at  knowledge  which  has 
some  direct  application. 

Moreover,  in  the  opinion  of  the  Sophists,  the  same  state 
of  things  exists  with  regard  to  our  moral  ideas.  There 
is  no  standard  of  right  and  wrong,  just  as  there  is  no  stand- 
ard of  truth  and  falsehood.  Each  man  has  the  right 
to  choose  what  he  regards  as  most  advantageous  for  himself. 
The  traditional  rules  of  morality  have  no  authority  over 
the  individual,  nor  is  it  possible  to  discover  any  rules  of 
morality  which  are  binding  on  all  men.  It  is  the  part  of 
wisdom  to  consult  one's  own  interest  in  acting,  and  to  seek 
to  secure  one's  own  advantage.  Moral  distinctions,  like 
logical  distinctions,  are  purely  relative  and  individual. 

Socrates  was  the  great  opponent  of  this  doctrine  of  scep- 
ticism and  relativity  as  taught  by  the  Sophists.  They  had 
concluded,  from  the  diversity  of  individual  opinion  on 
moral  questions,  that  there  is  no  real  or  absolute  distinction 
between  right  and  wrong,  false  or  true.  Socrates,  however, 
was  convinced  that  if  one  examined  more  carefullv  the 
nature  of  the  judgments  which   are   passed   by   differem 


22      Important  Stages  in  the  Development  of  Logic 

individuals,  one  would  find  common  elements  or  ideas.  I\ 
is  possible,  he  believed,  to  find  a  definite  standard,  both  in 
matters  of  theory  and  in  matters  of  practice.  This  common 
element,  however,  is  not  to  be  discovered  in  sensation,  or 
in  feelings  of  pleasure  and  pain;  these  experiences  are  purely 
individual,  and  can  never  serve  as  a  universal  standard. 
But  beneath  the  diversity  of  sensation  and  feelings  there 
is  the  thought,  or  concept,  which  is  common  to  all  men. 
When  rational  beings  come  to  understand  one  another,  they 
must  agree  as  to  the  nature  of  the  fundamental  virtues,  — 
justice,  temperance,  courage,  etc.  It  is  true  that  few  men 
have  thought  about  these  matters,  and  are  able  to  express 
their  meaning  clearly,  but  every  man,  as  a  rational  being, 
carries  these  fundamental  notions  in  his  mind.  Now,  in 
order  to  refute  the  moral  scepticism  of  the  Sophists  (and 
it  was  this  side  of  their  teaching  which  Socrates  especially 
opposed),  it  is  necessary  that  the  ethical  notions,  or  con- 
cepts, which  are  implicit  in  the  minds  of  men  shall  be  drawn 
out  and  carefully  defined.  How  is  this  to  be  accomplished? 
Socrates  did  not  undertake  to  teach  men  what  ideas  they 
should  hold  regarding  the  nature  of  any  of  the  virtues;  he 
rather  made  them  partners  in  an  investigation,  and  by 
means  of  skilful  questions  tried  to  assist  them  in  discovering 
the  real  nature  of  goodness  for  themselves.  Another  point 
to  be  noticed  is  that  the  definition  of  the  various  virtues 
was  reached  as  a  result  of  comparing  the  views  of  a  number 
of  individuals.  In  this  way,  by  comparing  the  opinions 
of  many  men  of  different  professions  and  of  different 
grades  of  society,  he  was  able  to  separate  what  was  merely 
individual  and  relative  in  these  opinions  from  what  was 
unchanging  and  absolute. 


§  6.   Aristotle  and  the  Syllogism  23 

Plato,  the  disciple  of  Socrates,  continued  the  work  of 
his  master.  He  did  not  confine  his  attention  wholly  to 
the  moral  conceptions,  but  showed  that  the  Socratic  method 
could  also  be  used  to  refute  the  intellectual  scepticism  of 
the  Sophists.  In  other  words,  he  proved  that  in  the  concept, 
or  thought,  as  opposed  to  sensation,  a  standard  of  truth 
is  to  be  found,  as  well  as  a  standard  of  morality.  Know- 
ledge arises  from  thinking,  and  it  is  possible  to  compare  our 
thoughts,  and  thus  to  reach  what  is  objective  and  real  in 
itself,  however  impossible  it  may  be  to  find  any  basis  of 
comparison  in  our  sensations.  In  Plato's  Dialogues  a  great 
many  logical  questions  come  up  for  discussion,  and  in  these 
discussions  we  can  often  see  some  of  the  fundamental  dis- 
tinctions of  present  day  thought  and  language,  as  it  were, 
in  the  making.  But  Plato  made  no  attempt  to  organize 
and  arrange  these  results  into  a  single  science. 

§  6.  Aristotle  and  the  Syllogism.  — This  work  of  organi- 
zation was  accomplished  by  Plato's  disciple,  Aristotle.  He 
undertook  a  thorough  investigation  of  the  process  of  reason- 
ing, and  sought  to  show  what  conditions  and  principles  are 
necessarily  involved  in  reaching  certainty.  Aristotle  was 
thus  the  founder  of  logic,  as  well  as  of  psychology,  zoology, 
and  most  of  the  other  sciences  which  have  come  down  to  us 
from  the  ancient  world.  His  most  important  logical  works 
are  the  Categories,  De  Inter pretatione,  Prior  Analytics,  Pos- 
terior Analytics,  Topics,  and  the  Sophistical  Elenchus,  a 
treatise  on  Fallacies.  These  writings  came  afterwards  to  be 
known  as  the  Organon  (or  scientific  instrument)  of  Aristotle. 
They  contained,  in  the  first  place,  what  we  call  theory  of 
knowledge  (a  discussion  of  the  structure  of  knowledge,  and 
of  the  scientific  principles  upon  which  it  rests) ,  which  formed 


24      Important  Stages  in  the  Development  of  Logic 

an  essential  part  of  Aristotle's  philosophical  system.  Bin 
they  also  furnished  the  practical  application  of  these  prin- 
ciples. In  his  doctrine  of  the  syllogism,  which  is  found 
mainly  in  the  Prior  Analytics,  he  showed  what  are  the  only 
valid  forms  of  reasoning  from  general  propositions,  and  thus 
furnished  the  pattern  or  type  to  which  all  such  proofs  must 
conform.  He  also  classified,  in  his  work  on  Fallacies,  the 
various  species  of  false  reasoning,  and  showed  how  false 
arguments  could  be  refuted  and  exposed  by  the  principles 
which  he  had  discovered.  The  form  to  which  Aristotle 
maintained  that  all  true  reasoning  can  be  reduced  was  as 

follows:  — 

All  men  are  mortal, 

Socrates  is  a  man, 

Therefore  Socrates  is  mortal. 

This  is  called  a  Syllogism,  and  it  is  made  up  of  three  propo- 
sitions. The  first  two  propositions  are  called  Premises,  and 
the  last  the  Conclusion.  All  reasoning  from  premises,  all 
proof,  can  be  reduced  to  this  form.  Of  course,  the  propo- 
sitions which  make  up  the  syllogism  do  not  always  stand 
in  this  order,  and  sometimes  one  of  them  may  be  omitted. 
Thus  in  the  argument:  '  he  ought  to  be  supported  by  the 
state,  for  he  is  an  old  soldier,'  the  conclusion  stands  first, 
and  one  premise  is  wanting  entirely.  It  is  easy  to  see,  how- 
ever, that  the  real  argument  when  properly  arranged  is 
equivalent  to  this:  — 

All  old  soldiers  ought  to  be  supported  by  the  state, 

He  is  an  old  soldier, 

Therefore  he  ought  to  be  supported  by  the  state. 

Now  the  part  of  Aristotle's  logic  which  was  best  worked 
out  was  a    theory  of  proof    or  demonstration  by  means 


§  6.    Aristotle  and  the  Syllogism  25 

of  the  syllogism.  Here  he  showed  clearly  the  various  ways* 
in  which  different  kinds  of  propositions  could  be  combined 
as  premises  to  yield  valid  conclusions,  and  proved  that  no 
conclusion  could  be  drawn  from  other  combinations.  This 
part  of  the  Aristotelian  logic  has  come  down  to  us  almost 
unchanged,  and  is  the  subject  of  Part  I.  of  the  present  volume. 

It  will  be  noticed  that,  in  the  doctrine  of  the  syllogism, 
Aristotle  was  dealing  with  that  kind  of  reasoning  which 
undertakes  to  demonstrate  the  truth  of  some  fact,  by  show- 
ing its  relation  to  a  general  principle  which  every  one  admits. 
In  other  words,  this  part  of  his  work  may  be  called  the 
logic  of  proof  or  demonstration.  Aristotle  was  at  one 
time  of  his  life  a  teacher  of  rhetoric,  and  he  seemed  always 
to  have  aimed  at  putting  this  art  of  reasoning  on  a  scien- 
tific basis.  That  is,  for  the  rules  of  thumb  and  questionable 
artifices  of  the  Sophists,  he  wished  to  substitute  general 
laws  and  methods  of  procedure  which  were  based  upon 
a  study  of  the  principles  and  operations  of  reason.  By 
complying  with  the  rules  which  he  laid  down,  an  argu- 
ment will  necessarily  gain  the  assent  of  every  rational  being. 

But  we  do  not  employ  our  reason  merely  in  order  to 
demonstrate  to  ourselves  or  to  others  what  we  already 
know.  We  seek  to  discover  new  facts  and  truths  by  its 
aid.  In  other  words,  we  not  only  wish  to  prove  what  is 
already  known,  but  also  to  discover  new  facts,  and  we 
need  a  logic  of  Discovery,  as  well  as  a  logic  of  Proof.  This 
distinction  between  proof  and  discovery  corresponds  in 
general  to  that  between  Deduction  and  Induction.  It  is  not 
an  absolute  distinction,  as  will  appear  later,  for  both  pro 
cesses  are  constantly  employed  in  conjunction.  But,  for  the 
present,  it  may  be  said  that  deduction  is  the  process  of  show- 


26      Important  Stages  in  the  Development  of  Logic 

ing  how  particular  facts  follow  from  some  general  principle 
which  everybody  admits,  while  Induction  shows  the  methods 
by  which  general  laws  are  obtained  from  an  observation  of 
particular  facts.  Now  Aristotle,  as  we  have  seen,  furnished 
a  very  complete  theory  of  Deduction,  or  method  of  proof. 
But  he  did  not  treat  of  Induction,  or  the  method  of  pass- 
ing from  particular  facts  to  general  laws,  with  anything 
like  the  same  completeness.  Moreover,  what  he  did  write 
on  this  subject  received  no  attention  for  many  centuries. 
Aristotle  was  himself  a  great  scientific  observer,  and  may 
well  be  regarded  as  the  father  of  many  of  our  modern 
sciences.  But,  in  his  logical  writings,  his  main  object  seems 
to  have  been  to  present  a  true  theory  of  argumentation,  as 
opposed  to  the  false  theories  of  the  Sophists.  Science,  too, 
was  only  in  its  beginning  when  Aristotle  wrote,  and  it  was 
impossible  for  him  to  foretell  the  methods  of  discovery 
which  it  has  actually  employed. 

After  Aristotle's  death  (322  B.C.),  and  after  the  loss  of 
Athenian  independence,  there  was  a  great  decline  of  interest 
in  matters  of  mere  theory  which  had  no  direct  application 
to  the  practical  affairs  of  life.  The  Stoic  school  did  make 
some  slight  additions  to  logical  theory,  but  like  their  oppo- 
nents, the  Epicureans,  they  regarded  practice,  the  art  of 
living  well,  as  the  supreme  wisdom  of  life.  The  Romans, 
who  derived  their  knowledge  of  Greek  philosophy  largely 
from  the  Stoics,  were  also  interested  in  the  practical  advan- 
tages of  logic,  rather  than  in  its  theoretical  side.  It  was 
the  possibility  of  applying  the  laws  of  logic  to  rhetoric  and 
public  speaking  which  especially  interested  Cicero,  who  was 
the  first  to  make  Latin  paraphrases  and  adaptations  of 
Greek  logic  in  his  rhetorical  works. 


I  6.   Ai'istotlc  and  the  Syllogism  2j 

For  more  than  seven  hundred  years,  during  the  Middle 
Ages,  the  Greek  language  and  literature  was  almost  unknown 
in  Western  Europe.  During  this  time,  almost  the  only 
sources  of  information  regarding  logic  were  Latin  trans- 
lations of  Aristotle's  Categories,  and  of  an  Introduction  to 
the  same  work  by  Porphyry,  who  lived  232-303  a.d.  Both 
of  these  translations  were  made  by  Boethius  (470-525), 
who  is  best  known  as  the  author  of  The  Consolations  oj 
Philosophy.  Even  when  scholars  again  became  acquainted 
with  the  original  works  of  Aristotle,  in  the  latter  part  of 
the  Middle  Ages,  they  did  not  really  understand  their  true 
significance.  They  took  the  husk,  one  may  say,  and  neg- 
lected the  kernel.  They  adopted  the  Aristotelian  logic 
as  an  external  and  arbitrary  set  of  rules  for  the  guidance 
of  thinking,  and  neglected  entirely  the  scientific  theory 
upon  which  these  rules  were  based.  A  great  deal  of  inge- 
nuity was  also  shown  in  subdividing  and  analyzing  all  possible 
kinds  of  argument,  and  giving  the  particular  rule  for  each 
case.  This  process  of  making  distinctions  was  carried  so  far 
that  scholastic  logic  became  extremely  cumbersome  and  arti- 
ficial. Its  pretensions,  however,  rapidly  increased  ;  it  claimed 
to  furnish  a  complete  instrument  of  knowledge,  and  a  sure 
standard  for  discriminating  between  truth  and  falsehood. 

It  is  not  very  difficult  to  understand  why  this  set  of  logical  rules 
seemed  so  satisfactory  to  the  age  of  Scholasticism.  The  men  of  this 
period  had  no  desire  to  increase  their  knowledge;  they  supposed 
that  they  were  already  in  possession  of  everything  which  was  worth 
knowing.  Their  only  object  was  to  weave  this  knowledge  into  a 
system,  to  show  the  connection  and  interdependence  of  all  its  parts, 
and  thus  to  put  it  beyond  the  possibility  of  attack.  And  for  this 
purpose  the  school  logic  was  admirably  adapted;   it  was  always 


?S      Important  Stages  in  the  Development  of  Logic 

possible  to  bring  every  case  which  could  arise  under  one  or  other  oi 
its  rules. 

There  is  no  doubt  that  the  Aristotelian  logic  had  a  real 
value  of  its  own,  and  that  it  exercised  a  very  important  influence 
upon  Western  civilization,  even  in  the  form  in  which  it  was 
taught  by  the  Schoolmen ;  but  there  is,  of  course,  nothing  com- 
plete or  final  about  it.  Its  main  purpose,  as  we  have  already 
seen,  was  to  furnish  a  method  by  means  of  which  the  knowledge 
we  already  possess  may  be  so  arranged  as  to  be  absolutely  con- 
vincing. But  the  centre  of  intellectual  interest  has  changed  since 
mediaeval  times.  We  are  not  content  merely  to  exhibit  the  cer- 
tainty and  demonstrative  character  of  the  knowledge  which  we 
already  have,  but  we  feel  that  there  is  a  great  deal  of  importance 
still  to  be  discovered.  So  that,  in  modern  times,  one  may  say 
the  desire  to  make  discoveries,  and  so  add  to  the  general  stock 
of  knowledge,  has  taken  the  place  of  the  media? val  ideal  of 
showing  that  the  traditional  doctrines  taught  by  the  church  are 
absolutely  certain  and  convincing.  And  when  men  became  con- 
scious of  the  importance  of  gaining  new  knowledge,  and  espe- 
cially knowledge  about  nature,  they  at  once  saw  the  necessity  for 
a  new  logic,  or  doctrine  of  method,  to  aid  them  in  the  under- 
taking. 

§  7.  Bacon  and  the  Inductive  Method.  —  All  the  great 
thinkers  of  the  sixteenth  and  seventeenth  centuries  saw 
clearly  that  the  school  logic  is  simply  a  method  of  showing 
the  certainty  of  the  knowledge  we  already  possess,  and 
does  not  aid  us  at  all  in  making  new  discoveries.  A  new 
method,  they  all  declared,  was  an  absolute  necessity.  The 
new  point  of  view  was  put  most  clearly  and  eloquently 
by  the  famous  Francis  Bacon  (1 561-1626),  at  one  time 
Lord  Chancellor  of  England.  Bacon  called  his  work  on 
logic   the   Novum  Organum,   thus  contrasting   it  with   the 


§  7-    Bacon  and  the  Inductive  Method  29 

Organon,  or  logical  treatises  of  Aristotle.  An  alternative 
title  of  the  work  is,  True  Suggestions  for  the  Interpretation 
of  Nature.  Bacon  begins  this  work  by  showing  the  ad- 
vantages to  be  gained  from  a  knowledge  of  nature.  It 
is  man's  true  business,  he  tells  us,  to  be  the  minister  and 
interpreter  of  nature,  for  it  is  only  by  becoming  acquainted 
with  the  laws  of  nature  that  we  are  ever  able  to  take  advan- 
tage of  them  for  our  own  ends.  "  Knowledge  and  human 
power  are  synonymous,  since  ignorance  of  the  cause  pre- 
vents us  from  taking  advantage  of  the  effect."  The  dis- 
covery of  the  laws  of  nature,  which  is  therefore  of  so 
great  practical  importance,  cannot  be  left  to  chance,  but 
must  be  guided  by  a  scientific  method.  And  it  is  such  a 
method  which  Bacon  endeavours  to  supply  in  the  Novum 
Organum. 

The  method  which  Bacon  proposed  seems  to  us  very 
simple.  If  we  would  gain  new  knowledge  regarding  nature, 
he  says,  and  regarding  natural  laws,  we  must  go  to  nature 
herself  and  observe  her  ways  of  acting.  Facts  about  nature 
cannot  be  discovered  from  logical  propositions,  or  from 
syllogisms;  if  we  would  know  the  law  of  any  class  of  phe- 
nomena, we  must  observe  the  particular  facts  carefully 
and  systematically.  It  will  often  be  necessary,  also,  to 
put  pointed  questions  to  nature  by  such  experiments  as 
will  force  her  to  give  us  the  information  we  want.  Know- 
ledge, then,  must  begin  with  observation  of  particular 
facts;  and  only  after  we  have  made  a  great  number  of 
particular  observations,  and  have  carefully  classified  and 
arranged  them,  taking  account  of  all  the  negative  cases, 
are  we  able  to  discover  in  them  the  general  law.  No  hypoth- 
eses or  guesses  are  to  be  made ;  but  we  must  wait  until  the 


30      Important  Stages  in  the  Development  of  Logic 

iabulations  of  the  particular  phenomena  reveal  the  general 
'form'  or  principle  which  belongs  to  them  all. 

It  will  be  frequently  necessary  to  refer  to  Bacon's  work  in 
what  follows.  At  present,  it  is  sufficient  to  note  that  Bacon 
showed  that  a  knowledge  of  nature  cannot  be  attained  through 
general  propositions  and  logical  arguments,  but  that  it  is 
necessary  to  begin  with  the  observation  of  particular  facts. 
He  emphasized,  also,  the  importance  of  systematic  obser- 
vation and  carefully  planned  experiments,  and  showed  that 
knowledge  must  begin  with  facts  of  perception.  This  is 
the  method  of  induction,  and  Bacon  is  usually  said  to  have 
been  the  founder  of  the  inductive  sciences  of  nature. 

Another  and  quite  different  method  of  extending  know- 
ledge was  proposed  by  the  great   Frenchman,   Descartes 
(1596-1650),  who  took  mathematics  as  the  type  to  which 
all    knowledge    should    conform.    That    is,    he    supposed 
that  the  true  method  of  extending  knowledge  was  to  begin 
with  general  principles,  whose  truth  could  not  be  doubted, 
and   to  reason  from    them  to  the    necessary  character  of 
particular    facts.     Descartes    and    his    followers    thought 
that  it  was  possible  to  discover  certain  axiomatic  propo- 
sitions from  which  all  truth  could  be  derived  through  reason. 
They  thus  emphasized  Deduction  rather  than  Induction, 
and   reasoning   rather   than   observation    and   experiment. 
The  spirit  of  Bacon's  teaching  was,   however,   continued 
in  England  by  John  Locke,  in  the  Essay  Concerning  Human 
Understanding    (1690).     During  the  next  centuries,  philo- 
sophical   thinkers    were   divided    into    two   great   schools: 
Rationalists,  or  those  who  agreed  in  the  main  with  Des- 
cartes ;  and  Empiricists,  or  Sensationalists,  who  followed  the 
teachings  of  Bacon  and  Locke. 


§  7-   Bacon  and  the  Inductive  Method  31 

Although    the    natural    sciences    made    great    advances 
during    the    seventeenth    and    eighteenth    centuries,    there 
seems  to  have  been  no  effort  made  to  analyze  and  describe 
the    methods    which    were    actually    being    employed.     In 
England,  at  least,  it  seems  to  have  been  assumed  that  all 
discoveries  were  made  by  the  use  of  the  rules  and  methods 
of  Bacon,     One  of  the  first  writers  to  attempt  to  explain 
the  method  used  by  the  natural  sciences  was  Sir  John  Her 
schel    (1792-1871).     His  work,  Discourse  on  the  Study  of 
Natural  Philosophy,  was  published  in  1832.     A  little  later, 
and  with  the  same  object  in  view,  William  Whewell  (1794- 
1866),   afterwards  Master  of  Trinity  College,  Cambridge, 
undertook    his   History   of  the  Inductive   Sciences,    which 
was  followed  some  time  after  by  the  Philosophy  of  the  Induc- 
tive Sciences.    The  man,  however,  who  did  most  towards 
putting  the  study  of  logic  on  a  new  basis  was  John  Stuart 
Mill  (1806-1873),  the  first  edition  of  whose  Logic  appeared 
in  1843.     We  shall  have  frequent  occasion  to  refer  to  this 
work   in  future  discussions.     It   is  sufficient  to  say  here 
that  Mill  continues  the  empirical  tradition  of  the  earlier 
English  writers  in  his  general  philosophical  position.    Mill's 
book  gave  a  great  impulse  to  the  study  of  logic.     Before 
it  was  published,  writers  on  the  subject  had  confined  their 
attention  almost  exclusively  to  the  syllogistic  or  deductive 
reasoning.    Mill,  however,  emphasized  strongly  the  impor- 
tance of  induction;    indeed,  he  regarded  induction  as  the 
or>ly  means  of  arriving  at  new  truth,  the  syllogism  being 
merely  a  means  of  systematizing  and  arranging  what  we 
already  know.    Though  few  logicians  of  the  present  day 
adopt  this  extreme  view,  the  importance  of  inductive  methods 
of   reasoning,  and    the    necessity  of    studying   them,  have 


32       Important  Stages  in  the  Development  of  Logic 

now  become  generally  recognized.  Most  modern  writers 
on  logic  devote  a  considerable  amount  of  attention  to  induc- 
tion. The  reader  will  find  that  Part  II.  of  the  present  volume 
deals  with  this  subject. 

§  8.  Logic  from  the  Evolutionary  Standpoint.  — There 
is  still  another  side  of  logic  which  has  been  developed 
in  the  English-speaking  world  since  the  time  of  Mill,  though 
it  is  a  direct  continuation  of  the  movement  started  in  Ger- 
many by  Kant  more  than  a  hundred  years  ago.  The  so- 
called  'modern'  logic  has  laid  aside  the  formalism  and 
paradoxical  mode  of  expression  adopted  by  Hegel,  but 
the  fundamental  conception  with  which  it  works  —  that  of 
development — is  essentially  the  same  as  that  employed 
by  the  latter  in  his  Wissenschaft  der  Logik  (1816-1818). 
It  is,  of  course,  true  that  the  work  of  Darwin  in  biology  and 
the  rapid  extension  of  the  evolutionary  method  tended  to 
make  the  older  idea  of  development  more  concrete  and 
render  it  more  attractive.  Moreover,  evolutionary  studies, 
particularly  in  psychology  and  anthropology,  have  contrib- 
uted directly  to  genetic  logic.  For  logic,  from  this  stand- 
point, seeks  to  describe  and  explain  intelligence  in  terms 
of  its  own  development.  It  looks  at  the  logical  mind  as  a 
system  of  functions  or  activities  that  have  a  work  to  do 
and  that  progressively  develop  in  the  capacity  to  perform 
that  work. 

The  Aristotelian  doctrine  of  the  syllogism  is  a  purely 
formal  science.  In  the  form  in  which  it  is  represented 
in  ordinary  text-books,  it  might  perhaps  be  more  prop- 
erly described  as  the  art  of  arranging  our  knowledge  in 
such  a  way  as  to  compel  assent.  The  '  matter  '  with  which 
thought  is  supposed  to  work  is  supplied  to  it  in  form  of 


§  8.  Logic  from  the  Evolutionary  Standpoint        33 

concepts  and  judgments.  The  problem  which  formal 
logic  has  to  solve  is  to  define  and  classify  the  various  kinds 
of  concepts  with  which  thought  operates,  and  to  determine 
the  various  relations  in  which  these  stand  when  combined 
into  judgments.  Similarly,  it  has  to  show  what  combi- 
nations of  judgments  can  be  employed  as  premises  leading 
to  valid  conclusions  in  the  syllogism.  The  criterion  of 
truth  employed  in  these  investigations  is  the  principle 
of  non-contradiction  or  consistency.  Inconsistent  com- 
binations of  concepts,  that  is,  are  ruled  out ;  but  so  far  as 
the  doctrine  of  the  syllogism  goes,  anything  is  true  which 
is  not  self-contradictory. 

Now,  without  questioning  the  practical  value  of  its  canons, 
it  is  obvious  that  formal  or  syllogistic  logic  does  not  take 
any  account  of  many  of  the  processes  of  everyday  thought, 
and  that  its  rules  go  but  a  little  way  in  helping  us  to  dis- 
tinguish the  true  from  the  false.  For,  in  the  first  place, 
to  think  is  not  merely  to  combine  and  arrange  ideas  already 
in  our  possession.  This  might  enable  us  to  render  clearer 
and  more  definite  what  we  already  know,  but  would  never 
enable  us  to  gain  new  knowledge.  The  real  movement 
of  thought  —  as  opposed  to  its  merely  formal  procedure 
—  consists  in  the  formation  of  new  ideas  and  new  know- 
ledge through  actual  contact  with  ihe  world  of  experience. 
A  complete  account  of  the  intellectual  process,  then,  must 
deal  with  the  relation  of  the  mind  to  objects ;  it  must  in- 
vestigate the  various  activities  by  means  of  which  thought 
interprets  the  world  and  builds  up  the  various  sciences 
of  nature  and  of  man. 

The  recognition  of  the  importance  of  induction,  and 
of  the  necessity  of  studying  the  methods  of  the  inductive 


34      Important  Stages  in  the  Development  of  Logic 

sciences,  which  was  brought  about  by  Whewell,  Mill,  and 
others,  was  a  step  in  the  right  direction,  for  it  called  atten- 
tion to  a  kind  of  thinking  which  occupies  a  large  place  in 
our  intellectual  life,  and  also  gave  rise  to  a  truer  conception 
of  the  nature  of  thought  itself.  But  even  Mill  did  not  reach 
the  idea  which  guides  modern  logicians,  namely,  that  thought 
or  intelligence,  as  the  function  of  interpreting  reality,  is  one 
from  beginning  to  end ;  and  that  the  various  logical  opera- 
tions are  all  parts  of  one  whole,  or  rather,  are  ways  in  which 
intelligence  operates  in  different  circumstances,  or  at  differ- 
ent stages  of  its  development.  He  still  tended  to  treat  of 
logical  processes,  like  conception,  judgment,  and  reasoning, 
as  if  they  were  separate  and  distinct  processes,  each  existing, 
as  it  were,  on  its  own  account.  In  short,  we  may  say  that 
Mill  was  still  influenced  by  an  atomistic  and  static  view  of 
mind:  he  does  not  think  of  knowledge  as  essentially  all  of  a 
piece,  or  of  its  movement  or  history  as  that  which  reveals  its 
nature. 

As  opposed  to  the  conception  of  mind  as  made  up  of 
separate  ideas,  the  thought  by  which  modern  logic  is  domi- 
nated is  that  of  the  unity  and  continuity  of  all  intellectual 
life.  Thought  is  regarded  as  an  organic,  living  function 
or  activity,  which  remains  identical  with  itself  throughout 
all  its  developing  forms  and  phases.  The  problem,  accord- 
ingly, which  logic  must  set  before  itself  is  to  show  the  unity 
and  interrelation  of  all  of  the  intellectual  processes.  No 
one  of  the  steps  or  stages  in  this  process  can  be  completely 
understood  when  viewed  by  itself :  each  is  what  it  is  only  in 
and  through  its  connection  with  the  whole  of  which  it  forms 
a  part.  No  hard-and-fast  boundary  lines  are  to  be  drawn 
between  the  different  stages  of  the  reasoning  process,  but 


§  8.    Logic  from  the  Evolutionary  Standpoint        35 

it  must  be  shown  that  the  whole  nature  of  intelligence  is 
involved  more  or  less  explicitly  at  each  step.  So  far  only 
the  broad  outlines  of  this  theory  have  been  filled  in;  but 
the  conception  of  an  organism  whose  parts  are  developing 
in  mutual  relation  and  interdependence  promises  to  be 
as  fruitful  when  applied  to  logic  as  it  has  already  shown 
itself  to  be  in  the  other  sciences. 

Besides  the  ordinary  histories  of  philosophy  the  reader  may  con- 
sult for  the  history  of  logic:  Prantl,  Geschichte  der  Logik  im  Abend- 
lande,  4  vols.,  Leipsic,  1 855-1870;  which  extends,  however,  only  to 
the  close  of  the  mediaeval  period.  Harms,  Geschichte  der  Logik,  Berlin, 
1881.  Ueberweg,  System  der  Logik,  4th  ed.,  1874;  Eng.  trans,  of  3d  ed., 
London,  1874.  Adamson,  article  'Logic,'  in  the  Encyl.  Brit.,  9th  ed.  Sir 
William  Hamilton's  Lectures  on  Logic,  also  containing  much  historical 
information. 

Among  modern  works  on  logic,  the  following  may  be  mentioned: 
J.  S.  Mill,  A  System  of  Logic,  London,  1st  ed.,  1843;  9th  ed.,  1875. 
W.  S.  Jevons,  The  Principles  of  Science,  London,  1874;  2d  ed.,  1877. 
Also  by  the  same  author,  Studies  in  Deductive  Logic,  1880;  and  Pure 
Logic,  1890.  H.  Lotze,  Logik,  1874;  Eng.  trans.,  London,  1881  and 
1888.  W.  Wuhdt,  Logik,  3d  ed.,  1906-1907.  C.  Sigwart,  Logik,  2d  ed., 
1889-1893;    Eng.  trans.,  London  and  New  York,  1895. 

The  newer  development  of  logic  is  well  represented  by  F.  H.  Bradley, 
The  Principles  of  Logic,  London,  1886.  B.  Bosanquet,  Logic,  or  the  Mor- 
phology of  Knowledge,  London,  1888;  and  The  Essentials  of  Logic,  Lon- 
don and  New  York,  1895.  L.  T.  Hobhouse,  The  Theory  of  Knowledge, 
London,  1896,  may  also  be  mentioned  in  the  same  group  of  writers, 
although  he  has  been,  perhaps,  more  influenced  by  Mill  than  by  any  other 
writer.  J.  M.  Baldwin,  Thought  and  Things,  or  Genetic  Logic,  New 
York,  1 906-1907,  has  emphasized  especially  the  genetic  processes  through 
which  logical  thinking  is  built  up. 

"The  following  works,  among  others,  have  proved  useful  as  text- 
books: W.  S.  Jevons,  Elementary  Lessons  in  Logic,  London  and  New 
York,  1870.  A.  Bain,  Logic,  Deductive  and  Inductive,  New  York, 
1883.  J.  N.  Keynes,  Studies  and  Exercises  in  Formal  Logic,  4th  ed., 
London,  1906.  W.  Minto,  Logic,  Inductive  and  Deductive,  New  York, 
1894.     J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  New  York,  1905. 


PART    I.  — THE   SYLLOGISM 

CHAPTER    III 

THE    SYLLOGISM    AND    ITS    PARTS 

§9.  The  Nature  of  the  Syllogism.  — The  theory  of  the 
syllogism,  as  has  been  already  stated  (§  5),  was  first  worked 
out  by  Aristotle.  And  it  stands  to-day  in  almost  the  same 
form  in  which  he  left  it.  A  few  additions  have  been  made 
at  different  points,  but  these  do  not  affect  materially  the 
main  doctrine.  In  dealing  with  the  nature  of  the  syllogism, 
we  shall  first  try  to  understand  its  general  aim  and  purpose, 
or  the  results  which  it  seeks  to  bring  about.  We  shall  then 
have  to  analyze  it  into  the  parts  of  which  it  is  composed, 
and  to  examine  and  classify  the  nature  of  these  elements. 
Finally,  it  will  be  necessary  to  discover  what  rules  must 
be  observed  in  order  to  obtain  valid  conclusions,  and  to 
point  out  the  conditions  which  most  commonly  give  rise 
to  error  or  fallacy. 

In  the  first  place,  it  is  to  be  noticed  that  syllogistic  logic 
deals  with  the  results  of  thinking,  rather  than  with  the 
nature  of  the  thought-process.  Its  object  is  not  to  give 
an  account  of  the  way  in  which  thinking  goes  on,  but -to 
show  how  the  ideas  and  thoughts  which  we  already  possess 
may  be  combined,  so  as  to  lead  to  conclusions  which  are 
certain,  and  which  will  compel  assent.  The  ideas  which 
the    syllogism  uses  as  material  are  fixed  by  having  been 

36 


§  9-    The  Nature  of  the  Syllogism  37 

expressed  in  language.  Indeed,  it  is  largely  with  words, 
as  the  expression  of  thoughts,  that  syllogistic  logic  deals. 
Many  of  the  discussions  with  which  it  is  occupied  have 
reference  to  the  proper  interpretation  of  words  and  propo- 
sitions; and  the  rules  which  it  furnishes  may  be  taken 
as  directions  for  putting  together  propositions  in  such  a 
way  as  to  lead  to  a  valid  conclusion.  Nevertheless,  it  is 
important  to  remember  that  these  rules  are  not  arbitrary 
and  external,  but  find  their  justification  in  the  nature  of 
thought.  Indeed,  the  theory  of  the  syllogism,  when  rightly 
understood,  may  be  said  to  reveal  the  fundamental  charac- 
teristics of  the  process  of  intelligence.  For  it  brings  together 
facts  in  such  a  way  as  to  make  evident  their  interrelation 
and  dependence.  It  connects  a  judgment  with  the  grounds 
or  reasons  which  support  it,  and  is  thus  a  process  of  systema- 
tization.  In  order'  to  understand  the  significance  of  the 
rules  of  syllogistic  logic,  then,  it  will  frequently  be  necessary 
to  look  beyond  words  and  propositions  to  the  act  of  thought 
whose  results  they  express. 

A  great  deal  has  been  written  regarding  the  principles 
or  laws  of  thought,  which  are  employed  in  all  logical  reason- 
ing. It  seems  better,  however,  to  postpone  the  definite 
consideration  of  this  subject  until  the  student  has  learned 
more  about  the  various  operations  of  thought,  and  has  had 
some  practice  in  working  examples.  In  dealing  with  the 
nature  and  principles  of  thought,  in  the  third  part  of  this 
book,  it  will  be  necessary  to  discuss  this  question  at  length. 
Even  at  the  present  stage  of  our  inquiry,  however,  it  is 
important  to  notice  that  syllogistic  reasoning  presupposes 
certain  simple  and  fundamental  principles  of  thought  as 
the  basis  of  its  valid  procedure.     In  particular,  the  regular 


38  The  Syllogism  and  its  Parts 

syllogism  is  founded  on  a  principle  which  we  may  call 
the  law  of  Identity,  or  the  law  of  Contradiction,  according 
as  it  is  stated  affirmatively  or  negatively.  Stated  affirma- 
tively, this  so-called  '  law  '  simply  expresses  the  fact  that 
every  term  and  idea  which  we  use  in  our  reasonings  must 
remain  what  it  is.  A  is  A,  or  has  the  same  value  and  mean- 
ing wherever  employed.  The  law  of  Contradiction  expresses 
the  same  thing  in  negative  language.  A  cannot  be  both  B 
and  not  B.  If  any  term  is  taken  to  be  the  same  as  another  in 
one  connection,  it  must  always  be  taken  to  be  so  ;  if  it  is 
different,  this  relation  must  everywhere  be  maintained.  The 
data  or  materials  which  are  employed  in  the  syllogism 
are  ideas  whose  meanings  are  supposed  to  be  permanently 
fixed  and  expressed  in  words  which  have  been  carefully 
defined.  It  would  be  impossible  to  reason,  or  to  determine 
the  relation  of  our  ideas,  if  their  meaning  were  to  change 
without  notice,  or  if  the  words  by  means  of  which  they 
are  expressed  were  used  now  in  one  sense  and  now  in  another. 
It  is  true,  of  course,  that  our  ideas  regarding  the  nature  of 
things  change  from  time  to  time.  And,  as  is  evident  from 
one's  own  experience,  as  well  as  from  the  history  of  language, 
a  corresponding  change  takes  place  in  the  meaning  of  words. 
But  the  assumption  upon  which  syllogistic  reasoning  proceeds 
is  that  the  ideas  which  are  to  be  compared  are  fixed  for 
the  meantime,  and  that  the  words  by  which  they  are  ex- 
pressed are  used  in  the  same  sense  throughout  the  course 
of  the  argument.  The  laws  of  Identity  and  Contradiction 
are,  then,  simply  the  expression,  in  positive  and  negative 
form  respectively,  of  the  principle  of  consistency.  The  one 
fundamental  postulate  of  all  thought  is  that  it  must  be 
consistent  with  itself. 


§  io.    The  Parts  of  a  Syllogism  39 

We  may,  however,  have  formal  consistency  without  hav^ 
ing  real  truth.  It  is  quite  possible  that  all  the  require- 
ments of  the  syllogism  may  be  met  without  its  conclusions 
being  true  of  reality.  In  other  words,  an  argument  may 
be  formally  true,  but  really  false.  It  is  not  difficult  to 
understand  why  this  may  happen.  The  syllogism  accepts 
without  criticism  the  ideas  and  judgments  which  it  com- 
pares. These  data  are,  of  course,  the  product  of  previous 
acts  of  thinking.  But  in  proceeding  to  arrange  them  in 
syllogistic  form,  we  do  not  inquire  whether  or  not  they  are 
true,  i.e.  adequate  to  express  the  nature  of  the  things  for 
which  they  stand.  For  the  formal  purposes  of  the  syllo- 
gism it  is  only  essential  that  their  meanings  be  clearly  under- 
stood, and  that  these  meanings  be  regarded  as  fixed  and 
permanent. 

§  io.  The  Parts  of  a  Syllogism.  —  The  syllogism  may 
be  said  to  express  a  single  comprehensive  act  of  thought. 
We  may  define  the  reasoning  expressed  in  a  syllogism  as 
a  judgment  which  has  been  expanded  so  as  to  exhibit  the 
reasons  by  which  it  is  supported.     In  the  syllogism, 

The  geranium  has  five  pointed  sepals, 
This  plant  has  not  five  sepals, 
Therefore  it  is  not  a  geranium, 

we  may  say  that  we  have  the  judgment,  '  this  plant  is  not 
a  geranium,'  supported  by  the  propositions  which  precede 
it,  and  that  the  whole  syllogism  taken  together  expresses 
a  single  thought,  which  is  complete  and  self-sufficient.  It 
is  possible,  however,  even  when  one  is  dealing  directly 
with  the  process  of  thinking,  to  distinguish  in  it  different 
subordinate  steps,  various  stages  which   serve   as  resting- 


40  The  Syllogism  and  its  Parts 

places,  in  the  course  of  its  passage  to  the  complete  ana 
comprehensive  form  represented  by  the  syllogism.  But 
it  is  usual,  in  dealing  with  the  syllogism,  to  take  a  more 
external  view  of  its  nature,  and  to  regard  it  primarily  as 
made  up  of  words  and  propositions. 

In  this  sense,  a  syllogism  can,  of  course,  be  divided  into 
parts.  In  the  first  place,  it  is  composed  of  three  statements, 
or  propositions.  In  the  example  given  above  the  two 
propositions  which  stand  first  are  called  the  Premises, 
since  they  furnish  the  grounds  or  reasons  for  the  propo- 
sition which  stands  last,  and  which  is  known  as  the  Con- 
clusion. However,  it  is  not  true  that  we  always  find  the 
two  premises  and  the  conclusion  arranged  in  this  regular 
order  in  syllogistic  arguments.  Oftentimes  the  conclusion 
is  given  first.  Frequently,  too,  one  of  the  premises  is  not 
expressed,  and  has  to  be  supplied  in  order  to  complete  the 
argument.  Thus  the  statement,  '  he  must  be  more  than 
sixteen  years  of  age,  for  he  attends  the  university,'  is  an 
incomplete  syllogism.  The  conclusion,  as  will  be  readily 
seen,  stands  first.  There  is  also  only  one  premise  expressed, 
To  put  this  statement  in  the  regular  syllogistic  form  we 
have  to  supply  the  missing  premise  and  arrange  it  as 
follows :  — 

All  students  of  the  university  are  more  than  sixteen  years  of  age, 

He  is  a  student  of  the  university, 

Therefore  he  is  more  than  sixteen  years  of  age. 

When  one  of  the  premises  or  the  conclusion  is  not  ex- 
pressed, the  argument  is  called  an  enthymeme.  Such  an 
argument  is  defective  only  in  form:  the  missing  premise 
or  conclusion  is  really  present    and  operative  in  thought. 


§  io.    The  Parts  of  a  Syllogism  4/ 

It  is  of  great  importance  to  form  the  habit  of  making  cleai 
to  oneself  the  premises  by  which  any  conclusion  claims 
to  be  supported.  In  this  way  groundless  assumptions  are 
often  brought  to  light;  and  the  weakness  of  an  argument 
exposed.  Whenever  words  like  '  therefore,'  '  for,'  '  because,' 
'  it  follows,'  etc.,  are  used  in  their  proper  signification,  it 
is  possible  to  find  an  argument  composed  of  two  premises 
and  a  conclusion.  But  one  must  not  allow  oneself  to  be 
imposed  upon  by  the  mere  words,  but  must  insist  on  under- 
standing exactly  what  are  the  premises  in  the  case,  and 
how  the  conclusion  follows  from  them.  Not  only  may  some 
part  of  the  argument  be  taken  for  granted,  as  a  kind  of  tacit 
agreement,  but  oftentimes,  in  arguments  as  actually  used, 
there  is  a  considerable  amount  of  repetition  and  illustration 
of  the  principles  employed,  without  any  attempt  to  bring 
these  various  statements  into  relation  in  a  formal  way  as 
premises  of  a  syllogism.  To  reduce  such  arguments  to 
syllogistic  form  requires,  accordingly,  a  certain  amount  of 
interpretation  of  the  statements  they  contain,  involving 
oftentimes  both  condensation  and  rearrangement.  Such 
reduction  of  the  usual  extended  form  of  arguments  is  usually 
necessary  in  order  to  bring  out  clearly  their  essential  struc- 
ture—  the  premises  which  are  actually  employed  to  carry 
the  conclusion — and  to  estimate  accurately  their  logical  force 
and  value.  Take,  for  example,  the  following  passage  from 
Jonathan  Edwards  :  — 

Why  should  we  be  afraid  to  let  persons  who  are  in  an  in- 
finitely miserable  condition  know  the  truth,  or  bring  them  into 
the  light  for  fear  it  should  terrify  them  ?  It  is  light  that  must 
convert  them  if  they  are  ever  to  be  converted.  The  ease,  peace, 
and  comfort  which  natural  men  enjoy  have  their  foundation  in 


42  The  Syllogism  and  its  Parts 

darkness  and  blindness  ;  therefore  as  that  darkness  vanishes  and 
light  comes  in  their  peace  vanishes  and  they  are  terrified.  But 
that  is  no  good  argument  why  we  should  endeavor  to  hold  their 
darkness  that  we  may  uphold  their  comfort. 

This  may  be  reduced  to  the  form  of  two  syllogisms 
somewhat  as  follows :  — 

(0 

The  terror  of  sinners  is  what  dispels  their  blindness, 

Light  is  a  terror  to  sinners, 

Therefore  light  is  what  dispels  their  blindness. 

(2) 
What  dispels  blindness  is  really  a  benefit  to  sinners, 
Light  is  what  dispels  their  blindness, 
Therefore  light  is  a  real  benefit  to  sinners. 

It  is  necessary  to  carry  the  division  of  a  syllogism  still 
farther.  Every  logical  proposition  may  be  divided  into 
two  Terms,  and  a  Copula  or  connecting  link.  The  terms, 
which  are  the  extremes  of  the  proposition,  are  named  the 
subject  and  the  predicate.  Thus  in  the  proposition,  '  the 
fields  are  covered  with  snow,'  '  the  fields  '  is  the  subject, 
'  are,'  the  copula,  and  '  covered  with  snow,'  the  predicate. 
To  reduce  a  proposition  to  the  logical  form  in  which  it  is 
most  conveniently  treated,  it  is  necessary  to  express  it  in 
such  a  way  that  the  two  terms  are  united  by  some  part  of 
the  verb  '  to  be,'  preferably '  is  '  or  '  are.'  Thus  the  sentence, 
'  No  plant  can  grow  without  light  and  heat,'  would  be 
expressed  as  a  logical  proposition  in  the  following,  or  some 
similar,  form  :  '  No  plant  is  an  organism  which  can  grow 
without  light  and  heat.'  'Men  have  strong  passions'  may 
be  written,  'Men  are  beings  having  strong  passions.'  It 
is  always  well  to  reduce  a  sentence  to  some  such  form,  by 


§  io.    The  Parts  of  a  Syllogism  43 

substituting  for  the  verb  of  predication  some  part  of  the 

verb  '  to  be.' 

The  analysis  of  the  syllogism  gives  us  the  divisions  under 
which  it  is  convenient  to  treat  this  part  of  logic.  We  shall 
accordingly  deal  (i)  with  Terms,  (2)  with  Propositions, 
and  (3)  with  the  Syllogism  as  a  whole. 

These  divisions,  however,  are  only  made  for  the  sake 
of  convenience  in  treatment.  It  must  not  be  forgotten 
that  a  term  is  a  part  of  a  proposition.  To  understand 
the  nature  of  a  term,  it  is  necessary  to  consider  the  part 
which  it  plays  in  the  judgment  which  the  proposition  ex- 
presses. In  other  words,  the  function  of  the  term,  rather 
than  the  form  of  the  word  or  words  employed,  must  be 
considered.  It  is,  of  course,  true  that  we  naturally  and 
commonly  use  certain  word  forms  to  express  certain  kinds 
of  ideas,  just  as  in  the  grammatical  sentence  the  different 
'  parts  of  speech  '  —  nouns,  verbs,  etc.  —  have  each  a 
definite  and  comparatively  permanent  function.  But  even 
in  the  sentence  it  is  the  part  which  the  word  in  its  grammatical 
function  plays,  rather  than  its  form,  which  determines 
whether  it  is  to  be  classified  as  a  noun  or  an  adjective,  a 
preposition  or  a  conjunction.  In  dealing  separately  with 
terms,  as  we  propose  to  do  in  the  next  chapter,  we  shall 
be  occupied  to  a  large  extent  with  the  form  of  words  in  which 
certain  kinds  of  ideas  are  usually  expressed.  But,  as  the 
same  word  or  group  of  words  may  be  used  for  different 
purposes,  it  will  be  necessary,  in  order  to  understand  the 
meaning  of  terms,  to  refer  frequently  to  the  various  ways 
in  which  they  are  used  in  a  proposition. 

The  same  difficulty   exists  when   propositions  are  con- 
sidered by  themselves,  the  relation  to  the  complete  argument 


44  The  Syllogism  and  its  Parts 

oi  which  they  form  a  part  being  thus  ignored.  In  this  case, 
however,  the  results  of  the  isolation  are  not  so  apparent ; 
for  a  proposition  forms,  in  a  certain  sense,  a  whole  by  itself. 
It  is  the  expression  of  a  judgment  which,  as  we  shall  see 
later,  is  the  unitary  process  of  thought.  It  has  thus  a  sig- 
nificance of  its  own,  as  expressing  a  more  or  less  complete 
and  independent  act  of  thought.  Nevertheless,  it  must 
not  be  forgotten  that  its  independence  and  completeness  are 
only  partial  and  relative.  A  single  proposition  cannot 
stand  alone.  Taken  strictly  by  itself,  a  proposition  h 
only  a  fragment.  In  order  to  make  it  intelligible,  it  must 
be  brought  into  relation  with  the  other  propositions  which 
state  the  grounds  or  reasons  upon  which  it  rests,  or  the 
conclusion  which  it  helps  to  support.  The  logical  nature 
of  a  proposition  will,  therefore,  depend  upon  its  function 
in  an  argument,  and  in  treating  of  propositions  this  fact 
must  not  be  forgotten. 

§n.  Perception,  Conception,  and  Judgment. — Before 
beginning  our  examination  of  the  elements  of  the  syllogism, 
it  is  necessary  to  define  some  terms  that  describe  certain 
phases  or  modes  of  our  knowledge.  These  are  Perception, 
Conception,  and  Judgment.  Judgment  is  both  the  ele- 
mentary and  the  universal  form  of  knowing.  It  includes 
all  the  others,  and  uses  them  as  a  means  to  its  own  end  of 
attaining  truth.  It  may,  perhaps,  be  best  described  as  the 
interpreting  activity  of  the  mind.  At  all  the  stages  of 
experience  it  is  at  work,  construing  things  in  terms  of  ideas 
or  meanings,  transforming  old  ideas  in  the  light  of  new 
facts,  in  order  to  render  them  more  definite  and  more  con- 
sistent. Judgment  is  thus  the  form  of  the  general  intellec- 
tual activity.     To  know  anything  is  to  express  it  in  terms  of 


§  ii.    Perception,  Conception,  and  Judgment         45 

ideas,  to  qualify  it  in  our  thought  as  this  or  that,  as  belonging 
to  a  certain  class  of  things,  or  perhaps  as  differing  in  some 
respect  from  another  class  of  things.  But  it  must  not  be 
supposed  that  judgment  —  or  any  form  of  thinking  —  is 
concerned  only  with  our  own  ideas.  Judgment  is  the 
interpreting,  idealizing  response  of  the  mind  to  the  real 
world,  with  which  it  is  always  in  relation.  To  think  is  not 
to  play  with  our  own  ideas:  real  thinking  deals,  more  or 
less  directly,  with  a  world  of  real  objects  and  persons.  In 
the  process  of  judgment,  then,  reality  is  interpreted  and 
its  meaning  expressed  in  terms  of  ideas.  The  expression 
of  such  an  act  of  thought  is  a  proposition,  which,  as  we  have 
already  seen,  is  composed  of  a  subject  and  a  predicate  term 
related  by  means  of  a  copula. 

Now  the  terms  of  which  a  proposition  is  composed  may 
be  either  Percepts  or  Concepts,  i.e.  the  result  of  a  perceptive 
act  or  of  a  conception.  A  percept  is  the  result  of  the  mind's 
direct  mode  of  apprehending  real  things  as  distinct  indi- 
viduals. Hence  a  percept  always  refers  to  '  this  '  or  '  that/ 
some  distinct  individual  thing  having  its  own  place  in  space 
or  in  time.  Thus,  I  perceive,  or  have  a  percept  of,  the 
objects  in  this  room,  and  of  the  tree  which  I  see  through 
the  window.  Similarly,  one  may  perceive  the  particular 
states  of  consciousness  in  one's  mind.  A  concept,  on  the 
other  hand,  is  a  general  meaning  or  idea.  It  does  not  refer 
directly  to  some  one  object  of  sense.  It  is  not  an  individual 
embodiment  of  a  particular  thing,  but  is  a  thought-construc- 
tion, carrying  with  it  the  idea  of  a  general  nature  or  mean- 
ing which  may  apply  to  a  number  of  individuals.  Thus, 
my  direct  experience  of  the  individual  tree  at  which  I  am 
looking  is  a  percept,  the  general  idea  of  tree  which  I  use 


46  The  Syllogism  and  its  Parts 

when  I  say  '  trees  are  either  deciduous  or  evergreens '  is  a 
concept.  I  may  have  a  percept  of  the  statue  of  Liberty  at 
the  entrance  to  New  York  harbour ;  '  liberty/  on  the  other 
hand,  is  a  concept  made  up  of  a  more  or  less  definite  group 
of  meanings,  which  are  unified  and  held  together  by  the 
word  in  which  it  is  expressed. 

What,  now,  is  the  relation  between  the  percepts  and  con- 
cepts which  are  expressed  in  the  terms  of  a  proposition, 
and  the  judgment  which  is  represented  by  the  proposition 
as  a  whole  ?  In  the  first  place,  it  is  to  be  noted  that 
percepts  and  concepts  are  the  results  of  previous  acts  of 
judgment.  Ideas  are  formed  only  through  the  mind's  own 
act  of  interpretation  ;  they  never  pass  over  into  the  mind 
from  some  external  source  as  ready-made  objects.  Even 
in  the  case  of  perception,  where  the  object  seems  to  be  thrust 
upon  us,  a  little  reflection  will  show  that  the  judging 
activity  of  attention  is  involved,  selecting  and  arranging 
the  various  sensation  elements,  and  interpreting  them  as  the 
parts  of  a  single  concrete  object,  in  accordance  with  past 
experience.  A  concept  like  '  man  '  or  '  justice '  is  still 
more  obviously  a  thought  or  judgment  construction.  As 
expressed  in  words,  it  may  be  said  to  be  an  embodiment  of 
a  judgment  d_*  a  group  of  judgments. 

And,  in  the  second  place,  it  is  from  these  percepts  and 
concepts  that  new  judgments  proceed.  In  other  words, 
the  basis  of  our  thought  in  going  on  to  the  discovery  of 
new  facts  and  relations  is  what  we  already  know.  But 
what  we  already  know  at  any  time  is  summed  up  in  the 
ideas  we  possess,  that  is,  in  the  percepts  and  concepts  which 
have  been  formed  by  previous  acts  of  judgment,  and  em- 
bodied in  names.     In  the  development  of  our  knowledge, 


§  ii.    Perception,   Conception,  and  Judgment         47 

however,  we  are  constantly  discovering  that  our  knowledge 
on  this  or  that  point  is  unsatisfactory.  The  old  way  of 
thinking  is  perhaps  too  vague  and  indefinite  to  furnish  us 
with  a  satisfactory  rule  of  action,  or  it  may  be  perceived 
to  be  inconsistent  with  new  facts  that  have  arrested  our 
attention.  Indeed,  the  inadequacy  of  the  habitual,  accepted 
point  of  view  may  be  forced  upon  us  in  a  variety  of  ways. 
Frequently,  no  doubt,  the  occasion  is  furnished  by  some 
practical  necessity  of  action.  Necessity  is  oftentimes  the 
mother  of  invention,  and  the  spur  to  the  discovery  of  new 
theories  and  conceptions.  In  other  cases  the  stimulus  to 
criticise  our  old  conceptions  may  come  from  social  inter- 
course; the  conflict  of  our  views  with  those  of  people  with 
whom  we  converse,  or  whose  opinions  we  read,  first  arouses 
us  from  our  dogmatic  slumber.  More  rarely,  perhaps,  in 
the  case  of  ordinary  minds,  theoretical  interest  may  be 
aroused  without  any  external  occasion,  and  the  desire  for 
truth  and  consistency  may  itself  be  sufficient  to  lead  one 
to  reexamine  and  transform  one's  old  ideas.  Whatever  the 
stimulus,  thinking  is,  on  one  side,  a  process  in  which 
old  conceptions  are  recast,  and  accepted  truths  transformed, 
a  constant  process  of  change  in  which  the  old  conceptions 
are  superseded  and  destroyed.  The  old  terms,  both  per- 
cepts and  concepts,  which  form  the  starting-point  are  re- 
constituted through  a  new  act  of  judgment.  From  one 
point  of  view,  then,  it  may  be  said  that,  like  Kronos,  thought 
exists  by  devouring  its  own  children.  But  there  is  another 
side.  Thinking  is  a  process  of  conservation  as  well  as  of 
transformation.  The  old  ideas  are  not  entirely  destroyed 
and  displa.ed  by  the  new  judgment,  but  further  developed 
and  defined.     The  truth  which  they  contain  is  taken   up 


48  The  Syllogism  and  its  Parts 

and  preserved  in  the  later  judgment  or  series  of  judgments. 
Moreover,  as  we  have  seen,  the  results  of  these  judgments 
are  again  laid  down  as  new  thought -contents  embodied  in 
language,  and  these,  in  their  turn,  form  the  starting-point 
for  further  judgments.  These  two  aspects  or  moments  of 
thought,  then,  —  what  we  have  called  the  transforming 
and  the  conserving  functions, — mutually  presuppose  and 
imply  each  other.  They  are  not  distinct  and  independent 
mental  operations,  but  organically  related  moments  or 
phases  in  the  life  of  thought.  Perceptions  and  conceptions 
can  arise  only  through  judgments,  while  judgments  pre- 
suppose perceptions  and  conceptions  as  their  necessary  basis 
and  starting-point.  Thus  the  total  movement  of  the  whole 
thought-process  is  rightly  described  as  Judgment. 


CHAPTER   IV 

THE   VARIOUS   KINDS    OF  TERMS 

§  12.  Singular,  General,  and  Collective  Terms.  — A  logical 
term,  as  we  have  already  seen,  is  any  word  or  group  of  words 
which  can  be  used  as  the  subject  or  predicate  of  a  proposi- 
tion. It  is  only  in  propositions,  and  as  elements  of  propo- 
sitions, that  terms  have  any  assignable  meaning.  It  will 
be  impossible,  therefore,  to  fix  the  meanings  of  isolated 
terms  without  reference  to  the  way  in  which  they  are  used 
in  propositions.  In  dealing  with  terms  apart  from  propo- 
sitions, we  shall  be  concerned  mainly  with  different  classes 
of  words  and  the  meanings  which  they  usually  express. 

The  first  division  which  we  have  to  notice  is  that  into  Sin- 
gular or  Individual,  General,  and  Collective  terms. 

(i)  A  Singular  or  Individual  term  is  one  which  can  be 
applied  in  the  same  sense  to  but  a  single  thing.  The  main 
purpose  of  Singular  terms  is  to  refer  to,  or  identify,  some  thing 
or  experience  which  can  be  regarded  as  a  single  existence. 
Proper  names  are  all  singular.  It  is  true  that  proper  names 
are  sometimes  used  to  denote  a  class  of  objects,  as  e.g., '  a 
Daniel,'  '  a  Mephistopheles.'  But,  when  thus  employed, 
they  lose  their  real  character  as  proper  names.  That  is, 
their  function  is  no  longer  merely  to  identify  certain  indi- 
viduals by  naming  them,  but  to  describe  them  by  mentioning 
certain  qualities  or  characteristics  which  they  are  supposed 
to  possess.     But  the  ordinary  purpose  in  using  a  proper 

E  49 


50  The   Various  Kinds  of  Terms 

name  is  to  indicate  some  individual  to  whom  the  name 
belongs.     In  this  sense,  then,  proper  names  are  Singular. 

In  addition,  any  word  or  group  of  words  which  is  applied 
to  a  single  thing  may  be  regarded  as  singular.  And  by 
'  single  thing,'  we  mean  anything  which  is  thought  of  as 
one,  as  well  as  objects  which  are  perceived  through  the 
senses.  Thus,  '  the  waterfall  just  below  the  bridge,'  '  the 
thought  of  the  present  moment,'  are  singular  terms,  and  so, 
also,  are  words  like  '  justice,'  '  goodness,'  '  the  chief  end  of 
man.'  It  is  perhaps  more  doubtful  whether  we  should  call 
terms  such  as  '  whiteness,'  '  sweetness,'  singular,  since  we 
speak  of  different  degrees  and  kinds  of  whiteness  and  sweet- 
ness. The  question  would  have  to  be  decided  in  every 
case  by  reference  to  the  way  in  which  the  terms  are  employed 
in  propositions. 

(2)  A  General  term  is  a  name  which  is  capable  of  being 
applied  to  a  whole  group  of  objects.  It  is  not  limited,  like 
the  singular  term,  to  a  single  thing,  but  can  be  used  in  the 
same  sense  of  an  indefinite  number  of  units.  All  class 
names,  like  *  metal,'  '  man,'  '  works  on  logic,'  are  of  this 
character.  Thus  a  general  name  is  one  that  refers  to  a  group 
which  may  be  divided  into  smaller  groups,  or  into  individual 
units.  Thus  iron,  gold,  silver,  etc.,  are  '  metals,'  and 
A,  B,  and  C,  '  men.' 

A  Collective  term,  on  the  other  hand,  is  a  name  applied 
to  a  number  of  individual  things  when  taken  together  and 
treated  as  a  whole,  as  '  an  army,'  '  an  audience.'  It  is 
important  to  distinguish  carefully  between  general  and 
collective  terms.  A  general  term  is  a  name  which  applies 
equally  to  each  individual  of  the  group  ;  or,  in  other  words, 
it   is  used   of  the   individuals  distributively.     A  collective 


§  13.    Abstract  and  Concrete  Terms  51 

name  belongs  to  the  whole,  but  not  to  the  separate  parts  of 
the  whole.  Thus  we  say  that  '  soldier  '  is  a  general  name, 
and  is  used  distributively  of  each  man  in  a  regiment.  '  Regi- 
ment,' however,  is  a  collective  name,  for  it  applies  only  to 
the  whole  group,  and  not  to  the  individual  soldiers. 

Ambiguity  sometimes  arises  from  the  fact  that  the  English 
word  '  all'  is  used  in  both  of  these  senses.  That  is,  it  may 
mean  'all  taken  together'  or  '  each  and  every/  Thus  we 
can  say:  '  All  the  angles  of  a  triangle  are  less  than  two 
right  angles,'  and  '  All  the  angles  of  a  triangle  are  equal  to 
two  right  angles.'  In  the  former  sentence,  the  word  '  all  * 
is  used  distributively,  in  the  latter  collectively.  In  Latin 
two  different  words  are  used:  cuncti  expresses  the  collective 
sense  of  '  all,'  and  omnes  its  distributive  signification. 

It  is  worth  noticing  in  this  connection  that  it  is  the  use  which 
is  made  of  terms,  rather  than  the  form  of  the  words  composing 
them,  which  determines  their  logical  character.  Thus  terms  which 
are  collective  in  one  connection  may  be  general  in  another.  '  Regi- 
ment,' for  example,  is  a  collective  term  with  reference  to  the  soldiers 
which  compose  it,  but  general  when  used  as  a  common  term  for  a 
number  of  similar  divisions  of  an  army.  The  same  is  also  true  of 
terms  like  'grove,'  'mob,'  'class,'  etc.  Again,  collective  terms 
may  be  very  properly  regarded  as  singular  when  the  proposition 
in  which  they  are  used  emphasizes  the  unity  and  solidarity  of  the 
group.  A  proper  name  is  sometimes  applied  to  a  collection  of  in- 
dividuals that  are  permanently  united  or  that  have  acted  together 
on  some  historic  occasion,  as,  for  example, '  The  Fifth  Cavalry  Regi- 
ment,' 'The  Charge  of  the  Six  Hundred.' 

§  13.  Abstract  and  Concrete  Terms.  —  Terms  are  fur- 
ther divided  into  abstract  and  concrete  terms.  The  word 
'  abstract '   is  often  used  popularly  to  describe   anything 


52  The    Various  Kinds  of  Terms 

which  is  difficult  to  understand.  Etymologically,  it  signifies 
drawn  off,  separated  (abstraho,  to  draw  off,  take  away). 
We  may  distinguish  two  senses  in  which  the  word  is  used, 
both,  however,  being  derived  from  its  etymological  signifi- 
cation. 

(i)  A  term  is  called  abstract  when  it  refers  to  some  thing 
which  cannot  be  directly  perceived  through  the  senses, 
or  otherwise  directly  experienced  as  an  individual  object 
or  state,  and  concrete  when  such  form  of  experience  is  pos- 
sible. Thus  '  a  beech  tree,'  '  a  tall  man,'  '  a  sweet  taste/ 
being  names  of  things  which  can  be  perceived,  are  concrete. 
Words  like  '  sweetness,'  '  hardness,'  etc.,  have  no  objects 
of  immediate  experience  corresponding  to  them,  and  are  for 
this  reason  called  abstract.  The  same  is  true  of  terms  like 
'individuality,' '  equality,'  'justice,'  etc.  These  words  repre- 
sent objects  of  thought,  rather  than  objects  that  are  directly 
experienced.  There  may  be  cases  or  instances  of  '  equality/ 
'  justice,'  etc.,  which  fall  under  our  perception,  but  the 
real  object  to  which  these  words  correspond  is  not  a  thing 
which  can  be  perceived  through  the  senses  at  all.  Their 
reality  is  conceptual,  or  for  thought,  not  something  directly 
revealed  through  the  senses. 

It  is  important  to  notice  that  there  are  degrees  of  abstractness  in 
terms,  according  as  the  objects  for  which  they  stand  are  nearer  to,  or 
farther  removed  from,  ordinary  sense-perception.  All  general  or 
class  names  are  abstract.  One  cannot  point  to  a  single  object  to 
which  the  term  '  metal, '  for  example,  or  the  term  '  man'  corresponds. 
But  although  such  terms  have  no  direct  sensuous  object,  yet  we  feel 
that  they  stand  nearer  to  sense-perception,  and  are  therefore  less 
abstract  than  words  like  'animal,'  'inorganic  substance.'  These 
terms,  again,  are  perhaps  less  abstract  than  'energy,'  or  'spirit,' 


§  13.    Abstract  and  Concrete  Terms  53 

or  even  than  singular  terms  like  'justice,'  'the  ground  of  the  uni- 
verse,' etc. 

(2)  Again,  the  word  '  abstract  '  is  applied  to  any  object 
which  is  treated  apart  from  the  whole  to  which  it  belongs. 
Thus  it  would  be  an  abstraction  to  attempt  to  represent 
the  nature  of  a  leaf  in  complete  isolation  from  the  plant 
to  which  it  belongs,  or  to  consider  the  nature  of  a  man 
without  regard  to  the  social  institutions  —  family,  church, 
state,  etc.  — of  which  he  is  a  member.  Of  course,  it  is 
essential  when  dealing  with  a  complex  whole  to  analyze 
it  into  its  parts,  and  to  understand  just  what  is  the  nature 
of  each  part  when  taken  by  itself.  But,  in  order  to  compre- 
hend fully  the  nature  of  the  parts,  it  is  necessary  to  restore 
them  to  their  proper  setting,  and  to  see  their  relation  to  the 
concrete  whole.  In  this  sense  of  the  word,  then,  '  abstract ' 
applies  to  what  is  taken  out  of  its  proper  setting,  broken 
off,  and  considered  apart  from  the  things  to  which  it  is 
organically  related.  Concrete,  on  the  other  hand,  means 
what  is  whole  and  complete,  a  system  of  things  which 
mutually  support  and  explain  one  another. 

Since  science  has  to  analyze  things  into  their  elements, 
and  to  investigate  and  describe  these  elements  in  detail, 
it  is  impossible  entirely  to  avoid  abstraction.  But  it  is 
necessary,  in  order  completely  to  understand  the  nature 
of  a  complex  object,  that  the  abstractions  of  analysis  shall 
be  corrected.  In  other  words,  the  concrete  relations  in 
which  things  stand  must  not  be  ignored  in  investigating 
them.  The  conception  of  evolution  in  recent  times  has 
done  much  to  render  the  biological  sciences  more  concrete 
in  the  sense  in  which  we  are  now  using  the  term.  For  it 
has  substituted  for  the  old  method  of  treating  each  species 


54  The   Various  Kinds  of  Terms 

of  plant  and  animal  as  distinct  and  separate,  '  cut  off  from 
each  other  as  if  by  a  hatchet,'  the  view  that  all  organic 
beings  are  members  of  one  family,  and  can  be  properly  un- 
derstood only  in  their  relations  to  one  another  (cf.  pp.  74-75). 

It  is  interesting  to  notice  that,  from  this  point  of  view,  sense- 
perception  is  more  abstract  than  thought.  For  the  senses  represent 
things  in  isolation  from  each  other.  Each  thing  is  known  in  sense- 
perception  as  a  separate  individual,  occupying  its  own  space  and 
time,  and,  in  this  way,  cut  off  from  its  fellows.  It  is  the  business  of 
thought,  on  the  other  hand,  to  discover  the  relations  between  things, 
and  the  principles  according  to  which  they  are  united.  Thinking 
thus  overcomes  the  abstract  point  of  view  of  sense-perception  by 
showing  that  what  appear  to  the  latter  as  separate  objects  are 
really  closely  and  necessarily  connected  as  members  of  a  com- 
mon unity  or  system.  Each  science  takes  as  its  province  certain 
facts  which  resemble  one  another,  but  which  nevertheless  appear 
to  sense-perception  to  be  quite  independent.  It  attempts  by 
thinking  to  bring  these  facts  into  relation,  to  show  that  they  are 
all  cases  of  some  law,  that  there  is  a  common  principle  which  unites 
them  as  parts  of  a  whole  or  system.  The  law  of  gravitation,  for 
example,  expresses  the  unity  which  thought  has  discovered  in 
things  which  appear  to  sense-perception  as  different  as  the  falling 
of  an  apple,  the  movements  of  the  heavenly  bodies,  and  the  ebb 
and  flow  of  the  tides.  Scientific  knowledge,  then,  is  more  con- 
crete than  the  facts  which  we  learn  from  ordinary  sense-percep- 
tion, because  it  brings  to  light  real  unity  and  connection  in  facts 
which  appear  to  be  entirely  isolated  and  independent  from  the 
latter  point  of  view. 

In  employing  the  terms  '  abstract '  and  '  concrete  '  it 
is  of  the  utmost  importance  to  distinguish  the  two  signifi- 
cations of  the  words.  From  one  point  of  view,  as  we  have 
seen,  all  thought  terms  are  abstract,  as  opposed  to  words 


§  i4-   Positive  and  Negative   Terms  55 

which  refer  directly  to  objects  of  sense-perception.  In 
another  sense, '  abstract '  denotes  what  is  partial  and  incom- 
plete, what  is  taken  by  itself  and  out  of  relation  to  the  system 
of  things  to  which  it  belongs.  And,  since  the  real  connection 
and  relations  of  things  are  not  given  by  perception,  but 
have  to  be  discovered  by  thought,  the  knowledge  which  the 
latter  yields  is  more  concrete,  in  this  latter  sense  of  the  term, 
than  that  afforded  by  the  former. 

§14.  Positive  and  Negative  Terms. — The  distinction 
between  Positive  and  Negative  terms  is  very  obvious.  Posi- 
tive terms  express  the  existence  of  some  quality,  or  group 
of  qualities,  in  the  objects  which  they  denote;  as,  e.g., 
1  happy,'  '  good,'  '  equality,'  '  organism,'  etc.  A  Negative 
term,  on  the  other  hand,  indicates  the  absence  of  qualities 
or  properties  in  some  object;  '  bad,'  'unhappy,'  '  inorganic,' 
'  injustice,'  for  example,  are  negative  terms.  Negative 
terms  are  often  formed  from  positive  by  means  of  the  affix 
less,  as  in  '  hopeless,'  or  by  means  of  certain  prefixes,  of 
which  the  more  common  are  un,  in,  dis,  a,  anti.  Words 
which  are  positive  in  form  are,  however,  often  negative 
in  meaning,  and  are  used  as  the  contradictories  of  other 
terms.  Thus  '  ignorant  '  is  generally  regarded  as  the  nega- 
tive of  '  learned,'  '  darkness '  is  the  negative  of  'light,'  etc. 
It  is  not  always  possible,  however,  to  find  a  separate  word 
to  express  the  exact  opposite  of  every  positive  term.  Words 
are  used  primarily  to  express  the  presence  of  qualities,  and 
the  negative  idea  may  not  be  referred  to  so  frequently  as 
to  require  a  separate  word  to  express  it.  Thus  there  is  no 
independent  term  to  express  the  opposite  of  '  transferable,' 
but  by  employing  '  non  '  as  a  negative  prefix  we  obtain 
1  non-transferable.' 


56  The    Various  Kinds  of  Terms 

It  is  always  advisable  when  we  wish  to  limit  a  term  strictly  to  its 
negative  application  to  employ  not  or  non  as  a  prefix.  Words 
which  are  negative  in  form  frequently  have  a  more  or  less  definite 
positive  signification.  Jevons  points  out  that  words  like  'unloosed1 
and  'invaluable,' though  negative  in  form,  have  a  positive  meaning. 
But,  in  addition,  terms  like  'unhappy,'  'immoral,'  do  not  merely 
indicate  the  absence  of  positive  qualities,  but  also  express  some 
positive  properties  of  the  objects  to  which  they  are  applied.  We 
speak  of  a  person  'being  positively  unhappy';  and  we  employ 
'non-moral'  to  express  the  simple  negative  relation  rather  than 
'immoral.' 

On  the  other  hand,  there  are  certain  terms  which  are  positive  in 
form  that  express  the  absence  of  qualities  or  attributes.  Words  like 
'blind,'  'dumb,'  'maimed,'  orphaned,'  may  be  given  as  examples. 
These  are  often  called  Privative  terms,  rather  than  Negative,  the 
distinction  being  that  they  refer  to  qualities  or  attributes  which  the 
objects  to  which  they  are  applied  naturally  and  usually  have,  but  of 
which  they  have  been  deprived,  or  which  they  have  never  possessed. 
Thus '  blind,'  as  applied  to  a  man,  implies  that  he  has  lost,  or  is  desti- 
tute of,  the  ability  to  see  which  naturally  belongs  to  a  human  being. 

Again,  other  terms  seem  to  be  positive  and  negative  solely  in 
relation  to  each  other.  '  Element '  and  '  compound  '  are  related  as 
negatives  or  contradictories.  It  is  difficult,  however,  to  say  which 
term  is  in  itself  negative  or  positive. 

It  is  important  to  notice  the  distinction  between  the 
relation  in  which  positive  and  negative  terms  stand  to  each 
other,  and  that  expressed  by  words  which  have  to  do  with 
opposite  extremes  of  something  which  possesses  quality 
or  degree.  Positive  and  negative  terms  are  mutually 
Contradictory.  An  element  is  what  is  not  a  compound, 
'  dishonest  '  is  the  contradictory  of  '  honest,'  and  as  con- 
tradictories there  is  no  middle  ground  between  them.     What 


§  15.    Absolute  and  Relative   Terms  57 

is  not  an.  element  is  a  non-element  or  a  compound.  Con- 
trary terms,  on  the  other  hand,  express  a  great  difference 
of  degree  in  the  objects  to  which  they  refer.  Thus  '  foolish  ' 
is  the  opposite  of  '  wise,'  '  cold  '  the  opposite  of  '  hot,'  and 
'  bitter  '  of  '  sweet.'  But  there  is  always  the  possibility  of 
a  middle  ground  between  opposites.  We  cannot  say  that 
a  man  must  be  either  wise  or  foolish,  a  taste  either  sweet 
or  bitter.  The  logical  contradictory  of  '  wise  '  is  '  not-wise,' 
of  '  bitter '  is  '  not-bitter,'  etc.  Contrary  terms,  then, 
must  be  carefully  distinguished  from  contradictories,  and 
we  cannot  conclude  because  one  contrary  term  is  false  in 
a  given  case  that  the  other  is  necessarily  true  (cf.  §  25). 

§15.  Absolute  and  Relative  Terms.  —  Another  classi- 
fication of  terms,  which  is  usually  given  by  logicians,  is 
that  into  absolute  and  relative  terms.  An  Absolute  term 
is  one  which  refers  to  an  object  which  exists  by  itself,  and 
has  an  intelligible  meaning  when  taken  alone.  Thus  'tree,' 
'house,'  'the  State  of  New  York,'  are  examples  of  absolute 
terms.  A  Relative  term,  on  the  contrary,  is  a  name  which 
only  derives  a  meaning  from  its  relation  to  something  else. 
The  term  'parent,'  for  example,  cannot  be  thought  of  except 
in  relation  to  'child.'  Similarly,  'teacher'  is  relative  to 
'pupil/  and  'cause'  to  'effect.'  Relative  terms  usually  go  in 
pairs  and  are  known  as  Correlatives.  Adjectives,  as  well  as 
nouns,  may  be  related  in  this  way.  The  presence  of  one 
quality  or  characteristic  in  a  thing  frequently  implies  the 
presence  of  others.  Thus,  ignorance  and  superstition, 
sympathy  and  tolerance,  are  necessary  correlatives,  because 
the  one  involves  the  other,  or  is  invariably  connected  with  it. 
It  is,  of  course,  true  that  no  finite  thing  is  completely  absolute  or 
independent  of  other  things.     The  nature  of  each  thing  is  largely 


58  The   Various  Kinds  of  Terms 

determined  by  the  nature  of  the  other  things  with  which  it  stands 
in  relation.  A  tree,  for  example,  is  relative  to  the  seed  from  which 
it  sprang,  the  soil  in  which  it  grew,  the  sunshine,  rain,  etc.,  which 
accompanied  its  growth.  All  finite  things  have  a  beginning  and  an 
end,  and  are  also  influenced  throughout  the  whole  period  of  their 
lives  by  the  action  of  other  things.  They  are,  therefore,  not  com- 
pletely absolute  or  independent.  It  is,  however,  possible  to  make  a 
distinction  between  words  which  are  the  names  of  things  that  are 
comparatively  independent,  and  may  for  ordinary  purposes  be  con- 
sidered by  themselves,  and  those  which  have  only  a  meaning  when 
regarded  as  correlatives. 

§  1 6.  Extension  and  Intension  of  Terms.  —  In  the  fore- 
going sections  of  this  chapter  wre  have  explained  the  main 
distinctions  which  concern  the  various  kinds  of  terms  with 
which  logic  deals.  It  is  now  necessary  to  notice  two  different 
purposes  for  which  terms  are  employed.  In  the  first  place, 
terms  are  used  to  refer  to  things,  to  name  and  identify 
them.  Thus  'man'  refers  to  the  different  individual  men, 
John  Smith,  Thomas  Brown,  etc.,  as  well  as  to  the  various 
classes  of  men,  Caucasians,  Indians,  Mongolians,  etc.  As 
denoting  or  naming  objects,  whether  these  be  individual 
things  or  classes  of  things,  terms  are  said  to  be  employed 
in  Extension.  But  words  are  also  used  to  describe  as  well 
as  to  name.  That  is,  they  represent  the  qualities  or  attrib- 
utes belonging  to  things  for  which  they  stand.  They  are 
not  bare  names  without  signification ;  but,  as  the  expression 
of  ideas,  they  stand  for  certain  qualities  or  characteristics 
which  things  are  judged  to  possess.  'Man,'  for  example, 
is  not  merely  a  name  which  may  be  applied  to  individual 
human  beings  or  races  of  men ;  but  it  implies  that  the  objects 
so  named  have  certain  qualities,  such  as  animal  life,  reason, 


§  1 6.    Extension  and  Intension  of  Terms  59 

and  the  power  of  communicating  with  their  fellows.  When 
words  are  used  in  this  way  to  define  or  describe  things, 
rather  than  merely  to  name  them,  they  are  said  to  be  em- 
ployed in  Intension. 

The  terms 'Denotation' and 'Connotation'  were  used  by  Mill 
instead  of  Extension  and  Intension,  respectively,  and  have  been 
adopted  pretty  generally  since  his  time.  To  '  denote '  is  to  point 
out  or  specify  the  objects  for  which  a  term  stands ;  and  to '  connote' 
is  to  take  account  of  the  attributes  or  qualities  which  a  name  implies. 
The  words '  depth '  and '  range '  are  also  sometimes  used  as  synony- 
mous with  Extension,  and  '  breadth '  or  '  comprehension '  instead  of 
Intension.  The  terms  to  be  remembered,  however,  are  Extension 
or  Denotation,  and  Intension  or  Connotation. 

It  is  useful  to  accustom  ourselves  to  distinguish  these 
two  functions  or  uses  of  a  term,  —  to  notice,  that  is,  the 
things  or  classes  of  things  to  which  the  name  applies, 
and  also  to  reflect  upon  the  signification,  or  ways  of  judg- 
ing about  these  things,  for  which  the  name  stands.  The 
Extension  of  a  term,  as  has  been  said,  indicates  the  objects 
to  which  a  name  applies,  and  the  Intension  the  qualities 
or  attributes  which  it  signifies.  From  the  point  of  view  of 
extension,  therefore,  '  planet '  may  be  defined  by  mentioning 
the  names  of  the  various  planets,  Mercury,  Venus,  the  Earth, 
Mars,  etc.  Similarly,  a  term  like  'carnivora'  might  be  given 
in  extension  by  naming  seals,  bears,  weasels,  dogs,  wolves, 
cats,  lions,  etc.  Usually,  however,  we  define  from  the  point 
of  view  of  intension,  that  is,  by  stating  the  qualities  or  char- 
acteristics for  which  the  term  stands.  Thus  we  give  the 
intensive  meaning  of  '  planet,'  as  a  heavenly  body  which 
revolves  in  an  elliptical  orbit  around  the  sun.  '  Carnivora,' 
defined  from  the  same  point  of  view,  are  mammalian  verte- 


60  The    Various  Kinds  of  Terms 

brates  which  feed  upon  flesh.  It  is  not  unusual,  however,  to 
supplement  an  intensive  definition  by  turning  to  extension  and 
enumerating  examples.  Thus  we  might  add  to  the  definition  of 
'  carnivora  '  just  given  the  words,  '  as  lions,  tigers,  dogs,'  etc. 
It  is  sometimes  said  that  the  intension  and  extension  of  terms 
vary  inversely.  This  is  simply  an  attempt  to  give  a  mathemati- 
cal form  of  statement  to  the  fact  that  the  more  a  term  is  defined, 
or  limited,  by  the  addition  of  attributes,  the  fewer  are  the 
objects  to  which  it  applies.  'As  the  intension  of  a  term  is 
increased,  its  extension  is  diminished,  and  vice  versa,''  is  the 
form  in  which  the  relation  is  often  stated.  For  example,  let 
us  begin  with  some  class  name  like  '  animal,'  which  has  a 
great  extension,  and  add  a  new  attribute,  'rational.'  We 
get  '  rational  animal '  =  man.  This  term  now  applies  to 
a  much  smaller  number  of  individuals  than  '  animal.'  The 
extension  of  the  former  term  has  been  diminished,  that 
is,  by  increasing  the  intension.  If  we  add  to  '  man'  still 
another  attribute  like  '  white,'  we  again  lessen  the  number 
of  individuals  to  which  the  term  applies.  In  general,  then, 
it  can  be  seen  that  the  extension  of  a  term  is  lessened  as  it 
is  made  more  definite  by  the  addition  of  new  attributes. 
And,  conversely,  by  stripping  off  attributes,  by  '  decreasing 
the  intension,'  the  number  of  individuals  to  which  a  term 
applies  is  increased.  There  is,  however,  no  exact  ratio 
between  the  increase  or  decrease  of  intension  and  the  corre- 
sponding change  in  extension.  Indeed,  the  extension  of  a 
class  may  increase  greatly  without  any  loss  of  intension  on 
the  part  of  the  term  by  which  the  idea  is  expressed.  Thus 
the  meaning  or  intension  of  the  term  '  man'  has  not  lost, 
but  rather  gained,  during  the  last  hundred  years  by  the  in- 
crease of  population  throughout  the  world. 


5  1 6.    Extension  and  Intension  of  Terms  61 

In  general,  it  is  only  when  some  kind  of  a  formal  clas- 
sification is  instituted,  when  terms  are  taken  as  arranged  in 
order  of  subordination,  that  there  is  any  meaning  in  speak- 
ing of  their  extension  and  intension  as  in  inverse  relation. 

Extension  and  intension,  according  to  the  view  just  given, 
represent  two  different  uses  or  functions  of  terms.  Every 
term  denotes  some  object  or  group  of  objects  more  or  less 
directly,  and  at  the  same  time  connotes  or  signifies  certain 
qualities  or  attributes.  Sometimes  the  one  purpose,  some- 
times the  other,  is  the  predominant  one.  Proper  names, 
for  example,  are  used  primarily  to  denote  or  mark  out 
things,  and  do  not  directly  qualify  or  describe  them.  In 
the  proposition,  '  these  animals  are  all  vertebrates,'  the 
predicate  term  '  vertebrates  '  is  employed  less  as  a  name  of 
a  number  of  animals  than  as  a  description  of  their  qualities. 
Nevertheless,  in  both  these  cases  the  terms  employed  have  the 
double  function  of  naming  or  denoting  objects,  and  of  con- 
noting qualities. 

Mill,  however,  and  certain  other  logicians  who  follow 
him,  seem  to  make  an  absolute  distinction  between  con- 
notative  and  non-connotative  terms.  "  A  non-connotative 
term  is  one  which  signifies  a  subject  only,  or  an  attribute 
only.  A  connotative  term  is  one  which  denotes  a  subject, 
and  implies  an  attribute.  By  a  subject  is  here  meant  any- 
thing which  possesses  attributes.  Thus  'John,'  or  'Lon- 
don/ or  '  England,'  are  names  which  signify  a  subject 
only.  '  Whiteness,'  '  length,'  '  virtue,'  signify  an  attribute 
only.  None  of  these  names,  therefore,  are  connotative. 
But  '  white,'  '  long,'  '  virtuous,'  are  connotative.  The  word 
'  white '  denotes  all  white  things,  as  snow,  paper,  the  foam 
of  the  sea,  etc.,  and  implies  or,  in  the  language  of  the  school- 


62  The   Various  Kinds  of  Terms 

men,  connotes  the  attribute  whiteness.  .  .  .  All  concrete  gen* 
eral  names  are  connotative.  The  word  '  man,'  for  example, 
denotes  Peter,  James,  John,  and  an  indefinite  number  of 
other  individuals,  of  whom,  taken  as  a  class,  it  is  the  name. 
But  it  is  applied  to  them  because  they  possess,  and  to  signify 
that  they  possess,  certain  attributes." * 

There  is  no  real  ground,  I  think,  for  such  an  absolute 
distinction  between  connotative  and  non-connotative  terms, 
or,  as  we  may  call  them,  descriptive  and  non-descriptive 
terms.  Of  course,  it  is  true  that  some  terms  are  more  directly 
descriptive  than  others;  but  when  we  consider  the  use  or 
function  of  terms,  we  find  that  they  are  never  used  merely 
to  name  things,  or  merely  to  connote  attributes,  though  in 
certain  cases  the  former  purpose  is  the  primary  one,  and 
in  other  cases  the  latter  object  is  more  prominent.  Even 
when  proper  names  are  employed,  the  qualities  or  character- 
istics of  the  objects  named  are  indirectly  implied.  The  very 
fact  that  a  proper  name  is  given  to  an  object  implies  that 
it  possesses  a  certain  definitely  marked  individuality.  More- 
over, a  proper  name  when  used  intelligently  carries  with  it  some 
still  more  definite  information  regarding  the  qualities  of  the 
thing  to  which  it  is  applied,  as,  for  example,  whether  it  is  a 
name  of  a  person,  an  animal,  or  a  place.  And,  on  the  other 
hand,  every  term  has  an  application  to  real  objects,  and  so 
a  denotation,  though  this  reference  to  reality  is  often  indirect 
and  somewhat  indeterminate.  For,  without  the  assumption 
of  this  application,  no  term  could  be  a  part  of  an  intelligible 
proposition  or  represent  a  genuine  thought.  Every  term,  then, 
more  or  less  directly,  both  denotes  objects  and  connotes 
attributes. 

1  Mill,  Logic,  Bk.  I.,  Ch.  II.,  §  5. 


§  1 6.   Extension  and  Intension  of  Terms  63 

REFERENCES 

J.  S.  Mill,  Logic,  Bk.  I.,  Ch.  II. 
F.  H.  Bradley,  The  Principles  of  Logic,  pp.  iS5~I73- 
B.  Bosanquet,  Logic,  Vol.  I.,  pp.  46-71- 
"  "  The  Essentials  of  Logic,  Lecture  V. 

J.  N.  Keynes,  Studies  and  Exercises  in  Formal  Logic,  4th  edition 
Part  I.,  Chs.  I.  and  II. 


CHAPTER   V 

DEFINITION   AND   DIVISION 

§  17.  Fixing  the  Meaning  of  Terms.  —  We  have  already 
referred  to  the  necessity  of  definitely  fixing  the  meaning  of 
the  terms  which  we  employ  in  reasoning.  In  ordinary 
life,  words  are  frequently  used  in  a  loose  and  shifting  way, 
without  any  clear  conception  of  the  qualities  or  properties 
which  they  connote,  or  of  the  objects  to  which  they  apply. 
Logic  demands,  in  the  first  place,  that  we  shall  have  clear 
and  precise  ideas  corresponding  to  our  words,  and  that  the 
signification  and  scope  of  the  latter  shall  be  carefully  deter- 
mined. But  this  is  a  demand  to  which  little  attention 
is  paid  in  the  ordinary  affairs  of  life.  To  define  our  terms 
in  explicit  language,  or  even  to  make  clear  to  ourselves 
the  ideas  and  things  for  which  they  stand,  is  by  no  means  a 
natural  or  a  universal  mode  of  procedure,  but  something 
which  requires  a  distinct,  conscious  effort. 

Bacon,  Hobbes,  Locke,  Hume,  and  nearly  all  of  the 
older  philosophical  writers  have  warned  us  against  the  abuse 
of  words.  The  whole  matter  has  been  expressed  very  clearly 
by  Locke,  from  whom  I  quote  the  following  passage:  — 

"  For  he  that  shall  well  consider  the  errors  and  obscurity, 
the  mistakes  and  confusion,  that  are  spread  in  the  world 
by  an  ill  use  of  words,  will  find  some  reason  to  doubt  whether 

64 


§  \"J.    Fixing  the  Meaning  of  Terms  65 

language,  as  it  has  been  employed,  has  contributed  more 
to  the  improvement  or  hindrance  of  knowledge  amongst 
mankind.  How  many  are  there,  that,  when  they  would  think 
on  things,  fix  their  thoughts  only  on  words,  especially  when 
they  would  apply  their  minds  to  moral  matters;  and  who, 
then,  can  wonder  if  the  result  of  such  contemplations  and 
reasonings  about  little  more  than  sounds,  whilst  the  ideas 
they  annex  to  them  are  very  confused  and  very  unsteady, 
or  perhaps  none  at  all;  who  can  wonder,  I  say,  that  such 
thoughts  and  reasonings  end  in  nothing  but  obscurity  and 
mistake,  without  any  clear  judgment  or  knowledge  ? 

"This  inconvenience  in  an  ill  use  of  words  men  suffer 
in  their  own  private  meditations;  but  much  more  manifest 
are  the  discords  which  follow  from  it  in  conversation,  dis- 
course, and  arguments  with  others.  For  language  being 
the  great  conduit  whereby  men  convey  their  discoveries, 
reasonings,  and  knowledge,  from  one  to  another;  he  that 
makes  an  ill  use  of  it,  though  he  does  not  corrupt  the  foun- 
tains of  knowledge,  which  are  in  things  themselves,  yet  he 
does,  as  much  as  in  him  lies,  break  or  stop  the  pipes  whereby 
it  is  distributed  to  the  public  use  and  advantage  of  mankind." l 

The  remedy  for  the  obscurities  and  confusions  of  words  is 
to  be  found  in  clear  and  distinct  ideas.  We  must  endeavour 
to  go  behind  the  words  and  realize  clearly  and  distinctly 
in  consciousness  the  ideas  for  which  they  stand.  Now  the 
means  which  logic  recommends  for  the  attainment  of  this 
end  is  definition.  The  first  requirement  of  logical  reasoning 
is  that  terms  shall  be  accurately  defined.  There  are,  however, 
two  ways  in  which  the  meaning  of  a  term  may  be  defined 
or  explained.     Every  term,  as  we  have  already  seen  (§  16), 

1  Essay  concerning  Human  Understanding,  Bk.  III.,  Ch.  XL 
F 


66  Definition  and  Division 

may  be  regarded  either  from  the  point  of  view  of  intension, 
or  from  that  of  extension.  To  define,  in  the  usual  sense, 
is  to  explain  from  the  standpoint  of  intension,  to  state  the 
attributes  or  qualities  which  are  connoted  by  the  term.  The 
process  of  explaining  terms  with  reference  to  the  objects, 
or  classes  of  objects,  for  which  they  stand  is  known  as  Divi- 
sion. We  may  include,  then,  under  the  general  term  defini- 
tion, (i)  Intensive  definition,  or  definition  in  the  ordinary 
sense,  and  (2)  Extensive  definition  or  division. 

§  18.  Definition. — To  define  a  term  is  to  state  its  con- 
notation, or  to  enumerate  the  attributes  which  it  implies. 
Thus  we  define  a  parallelogram  as  a  quadrilateral  figure 
whose  opposite  sides  are  parallel.  A  distinction  is  often 
made  between  verbal  and  real  definition.  When  we  merely 
wish  to  explain  the  meaning  in  which  we  intend  to  employ 
some  term,  we  have  verbal  definition.  But  when  it  is  the 
purpose  of  our  assertion  to  state  the  real  nature  or  essential 
characteristics  of  some  object,  the  proposition  employed  is 
said  to  constitute  a  real  definition.  This  distinction,  though 
not  without  importance,  cannot,  I  think,  be  regarded  as 
ultimate.  For  we  never  define  a  word  or  term  for  its  own 
sake  merely,  but  in  order  to  understand  the  nature  of  the 
objects  to  which  it  refers.  Indeed,  a  mere  word,  apart 
from  its  uses,  or  from  the  things  for  which  it  stands,  has  no 
interest  for  us.  In  defining  a  term,  then,  we  are  always 
attempting  to  explicate  or  explain,  more  or  less  directly, 
the  nature  of  a  thing,  or  our  idea  about  a  thing. 

Nevertheless,  there  is  an  advantage  in  distinguishing 
propositions  whose  immediate  purpose  is  to  expound  the 
meaning  of  a  word,  from  those  which  assert  something 
directly  of  an  object.     'Monarchy  consists  in  the  authority 


§  1 8.    Definition  6 J 

of  one  man  over  others,'  may  be  regarded  as  a  verbal  defini- 
tion, because  the  purpose  of  the  proposition  is  simply  to  explain 
the  meaning  of  the  subject  term.  On  the  other  hand, '  iron  is 
malleable  '  is  a  real  definition  (though  not  a  complete  one), 
because  it  does  not  primarily  refer  to  the  signification  of  the  word 
'iron,'  but  to  the  real  object  to  which  the  name  is  applied. 

In  this  connection,  it  is  interesting  to  notice  that  a  proposition 
which  amounts  to  nothing  more  than  a  verbal  definition,  is  some- 
times put  forward  as  if  it  were  an  assertion  which  contained  some 
real  knowledge.  The  solemn  commonplaces  in  which  ignorant  per- 
sons delight  are  often  of  this  character.  '  A  republic  is  a  govern- 
ment by  the  people,'  '  a  just  man  will  do  what  is  right,'  '  if  it  rains, 
the  ground  will  be  wet,'  may  serve  as  examples.  The  mistake  in 
such  cases  consists  in  supposing  that  these  assertions  are  anything 
more  than  verbal.  "  Trifling  propositions,"  is  the  name  that 
Locke  gives  to  this  form  of  statement.  '  The  property  of  water 
is  to  wet,  and  fire  to  burn;  good  pasture  makes  fat  sheep,  and  a 
great  cause  of  the  night  is  the  lack  of  the  sun,'  are  Corin's  pro- 
found remarks  to  Touchstone,  in  summing  up  his  philosophy. 

There  are  two  points  of  view  from  which  the  subject 
of  definition  may  be  considered.  We  might  either  discuss 
the  best  method  of  obtaining  real  definitions  of  the  nature 
of  things,  or  might  confine  our  attention  to  the  requirements 
which  a  good  definition  has  to  fulfil.  A  person's  ability  to 
define  either  a  term,  or  the  thing  for  which  the  term  stands, 
depends,  however,  upon  the  possession  of  clear  and  distinct 
ideas  on  the  subject.  The  problem,  then,  as  to  the  best 
method  of  finding  definitions,  resolves  itself  into  an  inquiry 
concerning  the  means  to  be  used  in  obtaining  and  classi- 
fying our  ideas  in  general ;  and  the  answer  to  this  question, 
so  far  as  an  answer  can  be  given,  must  be  found  in  the  theory 


68  Definition  and  Division 

of  logic  as  a  whole.     In  our  treatment  of  the  subject  we  shall 
therefore,  confine  our  attention  mainly  to  a  consideration 
of  the  requirements  of  a  logical  definition,  and  the  rules 
which  must  be  observed  in  stating  it  in  language. 

Before  entering  upon  the  subject,  however,  it  is  interesting 
to  refer  briefly  to  the  method  proposed  by  Socrates  for  obtain- 
ing definitions.  Socrates,  as  we  have  already  seen  (§5),  was 
the  first  to  emphasize  the  necessity  of  defining  and  fixing  the 
meaning  of  familiar  terms.  He  found  that,  though  the  people 
of  Athens  were  constantly  using  terms  like  '  good,'  '  beautiful,' 
'  justice,'  and  '  temperance,'  none  of  them,  not  even  those  with 
the  greatest  reputation  for  wisdom,  were  able  to  give  any  clear 
and  consistent  statement  of  what  these  terms  implied.  Soc- 
rates himself  did  not  profess  to  be  wiser  than  the  rest,  but  he 
had  a  genuine  spirit  of  inquiry,  and  made  it  the  business  of  his 
life  to  try  to  arrive  at  clear  conceptions,  especially  with  regard 
to  certain  fundamental  ethical  virtues,  like  justice,  and  tem- 
perance, and  wisdom,  which  he  regarded  as  of  the  utmost 
practical  importance.  It  was  by  means  of  conversation  with 
others  that  he  sought  to  gain  clear  ideas  regarding  the  nature 
of  these  virtues.  By  a  series  of  questions  and  answers,  by  com- 
parison of  any  definition  proposed  with  particular  facts  which 
are  admitted,  he  led  his  interlocutors  to  expose  and  refute  the 
inadequacies  of  their  earlier  statements. 

This  method  of  proceeding  by  means  of  question  and 
answer,  and  thus  compelling  a  speaker  to  admit  particular 
facts  which  refute  the  general  thesis  which  he  is  maintaining,  is 
called  Dialectic.  This  was  the  means  by  which  Socrates  con- 
stantly strove  to  advance  to  consistent  and  adequate  defini- 
tions. Apart  from  the  dialectical  and  dramatic  form  which  the 
Socratic  argument  took,  the  method  employed  is  essentially 


§  1 8.    Definition  69 

that  of  induction.  For  the  definition,  or  conception,  is  derived 
from  a  comparison  of  particular  instances,  both  positive  and 
negative.  By  a  consideration  of  individual  cases,  Socrates 
sought  to  obtain  a  definition  which  would  be  a  complete  and 
adequate  expression  of  the  nature  of  all  the  individuals  which 
share  in  the  class  name.  Aristotle  says  that  it  is  to  Socrates 
we  owe  the  method  of  induction  and  logical  definitions. 
Clear  and  distinct  conceptions,  formulated  in  exact  definitions, 
constituted  the  scientific  goal  for  Socrates,  and  the  inductive 
procedure  of  observing  and  classifying  particular  instances 
was  the  means  which  he  employed  for  reaching  this  goal. 
It  should,  however,  be  added  that  the  Socratic  use  of  in- 
duction, as  Plato  represents  it  in  his  Dialogues,  is  more  often 
popular  in  character  than  strictly  scientific,  judged  by  our 
present  standards. 

The  second  question  has  reference  to  the  formulation  of  a 
definition  in  language.  Suppose  that  we  already  possess  a  clear 
conception  of  the  meaning  of  the  terms  to  be  defined,  what  are 
the  conditions  which  a  logical  definition  must  fulfil?  The 
answer  to  this  question  is  usually  given  in  logical  text-books 
by  means  of  a  set  of  rules  for  definition.  Before  stating  these 
rules,  however,  it  is  necessary  to  explain  the  meaning  of  the 
terms  '  genus  '  '  species,'  and  '  differentia,'  which  will  be  fre- 
quently employed  throughout  the  remainder  of  this  chapter. 
These  terms,  together  with  '  property  '  and  '  accident,'  consti- 
tute what  the  older  logicians  called  the  Predicables,  and  state 
all  the  possible  relations  which  a  predicate  may  express  with 
regard  to  a  subject.  It  will  only  be  necessary,  however,  for 
us  to  consider  briefly  the  signification  of  the  first  three  terms. 
In  logic,  any  term  may  be  regarded  as  a  genus  which  con- 


jo  Definition  and  Division 

tains  two  or  more  subordinate  classes  or  species.  A  species^ 
on  the  other  hand,  is  simply  a  subdivision  or  subordinate 
class  of  some  larger  whole.  Thus  '  metal '  is  a  genus  with 
reference  to  iron,  gold,  silver,  etc.,  which  are  its  species. 
'  Rectilinear  figure  '  is  the  genus  to  which  belong  the  various 
species,  triangle,  quadrilateral,  pentagon,  etc.  The  differentia 
of  any  term  is  made  up  of  the  qualities  or  characteristics  which 
distinguish  it  from  other  terms,  from  the  genus  to  which  it 
belongs,  as  well  as  from  the  species  which  are  coordinate  with 
it.  Thus  the  logical  differentia  of  a  triangle  is  the  property  of 
having  three  sides  ;  the  differentia  of  man  is  that  which  dis- 
tinguishes him  from  other  animals,  whether  this  be  the  power 
of  speech  and  reason,  or  some  other  characteristic,  either  physi- 
cal or  mental. 

The  use  of  the  terms  '  genus  '  and  '  species  '  in  logic  is  en- 
tirely relative.  That  is,  any  term  may  be  considered  either 
as  a  species  or  a  genus,  according  as  it  is  regarded  as  form- 
ing a  part  of  some  more  comprehensive  class,  or  as  itself 
including  other  classes.  Thus  man,  for  example,  is  a  species 
of  the  genus  'animal';  but  the  same  term  also  may  be 
regarded  as  a  genus  including  various  species  of  men,  Cauca- 
sians, Negroes,  Mongolians,  etc.  In  the  same  way, '  animal ' 
may  be  considered  a  species  of  the  still  more  comprehensive 
class '  organized  being, '  and  this  latter  term  again  as  a  speciesof 
the  genus  '  material  being.'  A  still  higher  or  more  comprehen- 
sive term  which  includes  as  its  species  material  and  spiritual 
beings  alike  is  '  being.'  Since  this  term  includes  everything 
which  exists,  and  can  therefore  never  be  included  in  any  more 
general  class,  it  is  sometimes  called  the  highest  genus  (sum- 
mum  genus).  On  the  other  hand,  we  might  proceed  down- 
wards until  we  come  to  a  class  which  does  not  admit  of  division 


§  1 8.    Definition  Ji 

into  any  subordinate  classes.     Such  a  term  is  called  in  logic 
the  lowest  species  (infima  species). 

It  is  important  to  notice  that  the  terms '  genus '  and '  species '  have 
not  the  same  signification  in  logic  as  in  the  natural  sciences.  In 
classifying  objects  in  natural  history,  we  use  the  terms  'variety,' 
'  species,' '  genus,' '  family,'  and '  order,'  to  denote  varying  degrees  of 
relationship  between  certain  groups  or  classes  of  objects.  These 
terms,  as  thus  employed,  also  indicate  certain  relatively  fixed  divi- 
sions, or  permanent  ways  of  grouping  the  various  forms  of  plant  and 
animal  life.  But  in  logic  the  terms  'genus'  and  'species'  are  em- 
ployed to  indicate  the  relationship  between  any  higher  and  lower 
class  whatsoever.  Moreover,  as  we  have  seen,  any  term  (excepting 
only  the  highest  genus  and  the  lowest  species)  may  be  regarded 
from  different  standpoints,  as  either  a  genus  or  a  species. 

We  shall  now  proceed  to  state  the  requirements  of  a  logical 
definition :  — 

(i)  A  definition  should  state  the  essential  attributes  of  the  thing 
to  be  defined.  This  is  done  by  stating  the  genus  to  which  the 
object  belongs,  and  also  the  peculiar  marks  or  qualities  by 
means  of  which  it  is  distinguished  from  other  members  of  the 
same  class.  Or,  as  the  rule  is  usually  stated :  A  logical  defini- 
tion should  give  the  next  or  proximate  genus,  and  the  differ- 
entia of  the  species  to  be  defined.  Thus  we  define  a  triangle 
as  a  rectilinear  figure  (genus)  having  three  sides  (differentia); 
and  man  as  an  animal  (genus)  which  has  the  power  of  speech 
and  reason  (differentia). 

(2)  A  definition  should  not  contain  the  name  to  be  defined, 
nor  any  word  which  is  directly  synonymous  with  it.  If,  for 
example,  we  were  to  define  justice  as  the  way  of  acting  justly, 
or  life  as  the  sum  of  vital  processes,  we  should  be  guilty  of  a 
violation  of  this  rule. 


72  Definition  and  Division 

(3)  The  definition  should  be  exactly  equivalent  to  the  class  oj 
objects  defined ;  that  is,  it  must  be  neither  too  broad  nor  loo  narrow. 
In  other  words,  the  definition  must  take  account  of  the  whole 
class,  and  nothing  but  the  class.  'A  sensation  is  an  elementary 
state  of  consciousness,'  for  example,  is  too  broad  a  definition, 
since  it  applies  equally  to  affective  and  conative  elementary 
processes.  On  the  other  hand,  the  definition  of  government 
as  '  an  institution  created  by  the  people  for  the  protection  of 
their  lives  and  liberties,'  is  too  narrow.  For  it  takes  no 
account  of  absolute  forms  of  government  which  do  not  depend 
upon  the  will  of  the  people.  Each  of  these  cases  may  be 
regarded  as  a  failure  to  give  the  true  differentia  of  the  class 
to  be  defined,  and  hence  as  violations  of  the  first  rule. 

(4)  A  definition  should  not  be  expressed  in  obscure,  figurative, 
or  ambiguous  language.  The  reasons  for  this  rule  are  at  once 
evident.  Any  lack  of  clearness  or  definiteness  in  a  definition 
renders  it  useless  as  an  explanation.  Sometimes  the  words 
used  in  defining  may  be  less  familiar  than  the  term  to  be  ex- 
plained (ignotum  per  ignotius).  The  definition  which  was 
once  given  of  the  word  '  net '  as  '  a  reticulated  texture  with 
large  interstices  or  meshes,'  may  serve  as  an  example. 

(5)  A  definition  should,  whenever  possible,  be  affirmative, 
rather  than  negative.  A  definition,  that  is,  should  state 
what  a  term  implies,  rather  than  what  it  does  not  imply. 
Sometimes,  however,  the  purpose  of  a  definition  may  be  best 
attained  by  a  negative  statement  of  what  is  excluded  by  the 
meaning  of  the  term.  Thus,  for  example,  we  may  define  a 
spiritual  being  as  a  being  which  is  not  material,  that  is,  unlike 
a  material  body  made  up  of  parts  extended  in  space.  This 
is  an  exception  to  the  rule.  But  it  should  be  noted  that  there 
are  other  definitions  which,  while  negative  in  form,  are  not 


§  1 8.   Definition  73 

really  exceptions  to  it.  Such,  for  instance,  is  the  definition  of 
a  bachelor  as  an  unmarried  man.  This  is  a  precise  statement 
of  what  is  included  in  the  meaning  of  that  term.  It  is,  there- 
fore, the  meaning  rather  than  the  form  of  the  definition  to 
which  we  should  look  in  applying  this  rule.  The  fault  against 
which  it  is  directed  is  that  of  the  so-called  'infinite'  definition, 
which  merely  states  what  a  thing  is  not,  without  regard  to 
whether  such  a  negation  sensibly  increases  one's  knowledge  of 
the  meaning  of  the  term  or  not.  Such  a  definition  is  '  infinite' 
in  the  sense  that  to  enumerate  everything  that  the  term  to  be 
defined  is  not  would  be  an  infinite  process. 

(1)  A  logical  definition,  as  has  been  said,  requires  us  to  mention 
the  proximate  genus  or  next  higher  class  to  which  the  species  to  be 
defined  belongs,  and  also  the  specific  or  characteristic  differences 
which  distinguish  it  from  other  species.  Now  it  is  clear  that  there 
are  certain  cases  in  which  these  conditions  cannot  be  fulfilled.  In 
the  first  place,  no  logical  definition  can  be  given  of  the  highest  genus, 
because  there  is  no  more  general  class  to  which  it  can  be  referred. 
And,  again,  although  it  is  possible  to  give  the  differentia  of  any 
species  such  as 'man'  or  'metal,'  it  is  not  possible  to  state  indi- 
vidual characteristics  by  means  of  a  logical  definition.  An  indi- 
vidual thing  may  be  perceived,  and  its  various  properties  pointed 
out.  But  it  is  never  possible  to  state  in  a  logical  definition  wherein 
the  individuality  of  a  particular  thing  consists.  The  uniqueness  of 
a  particular  object  cannot  be  summed  up  in  a  general  definition,  but 
must  be  learned  through  perception.  We  may  perhaps  say  that  the 
highest  genus  is  above,  and  the  individual  thing  below,  the  sphere  of 
logical  definition. 

There  are,  moreover,  other  terms  such  as  'space,' '  time,' '  life,' 
'thought,'  which  are  not  readily  referred  to  any  higher  class,  and 
for  which,  therefore,  logical  definitions  cannot  be  given.  These 
terms  are  sometimes  said  to  denote  objects  which  are  sui  generis, 
or  of  their  own  class. 


74  Definition  and  Division 

(2)  This  use  of '  genus '  and  '  species '  in  definitions  comes  to  us 
from  the  logic  of  Aristotle.  The  purpose  of  definition,  as  we  have 
seen,  is  to  make  our  conceptions  clear  and  precise;  that  is,  the 
definition  should  state,  as  exactly  and  concisely  as  possible,  the 
essential  characteristics  of  the  thing  defined.  And  the  most  con- 
venient way  to  do  this  is  often  to  mention  some  more  inclusive 
group  of  objects,  the  general  nature  of  which  is  known,  and  at  the 
same  time  to  add  the  special  characteristics  which  distinguish  the 
thing  in  question  from  the  rest  of  this  group.  Thus,  for  example, 
it  is  much  more  convenient  to  define  a  dicotyledon  as  'a  plant 
with  two  cotyledons  or  seed  shoots'  than  it  would  be  to  enumer- 
ate all  the  special  characters  of  plants  as  well  as  the  distinctive 
character  of  the  germinating  seed. 

(3)  But  while  this  is  true  in  general,  it  should  not  be  supposed  that 
this  is  the  only  way  in  which  good  definitions  can  be  reached.  The 
purposes  and  methods  of  the  particular  science  or  study  employing 
the  definition  determine  both  its  content  and  the  proper  form  of  its 
statement.  The  definition,  by  giving  genus  and  specific  differentia, 
is  especially  useful  where  our  chief  purpose  is  one  of  classification, 
of  ranging  the  concepts  employed  in  any  subject  in  a  fixed  order  for 
further  reference  and  use.  But  it  is  often  true,  especially  in  the 
natural  sciences,  that  a  thing  may  be  better  defined  by  telling  how 
it  comes  into  being  than  by  giving  it  a  place  in  a  fixed  scheme  of 
classification.  This  second  mode  of  definition  might  be  called 
genetic  definition.  Its  use  is  frequent  where  we  are  concerned  with 
processes  and  the  laws  of  their  action,  and  it  often  represents  an  ad- 
vance in  knowledge  upon classificatory  definition.  To  define*  heat,' 
for  example,  as  '  a  force  in  nature  recognized  in  the  phenomena  of 
fusion  and  evaporation,  etc.,'  tells  us  less  about  its  real  nature  than 
the  statement  that  it  is c  a  form  of  energy  possessed  by  bodies  derived 
from  an  irregular  motion  of  their  molecules.'  To  define  '  water'  as 
1  a  fluid  which  descends  from  the  clouds  in  rain,'  is  less  adequate  for 
scientific  purposes  than  the  chemical  definition  of  it  as  'a  fluid 


§  1 8.   Definition  75 

formed  by  adding  one  part  of  oxygen  to  two  parts  of  hydrogen.'  In 
zoology  and  botany  the  older  definitions  of  animals  and  plants  by 
giving  their  genus  and  the  distinctive  or '  diagnostic '  marks  by  which 
their  respective  species  might  be  recognized,  received  a  new  meaning 
in  the  light  of  the  theory  of  evolution ;  for  these  classificatory  relation- 
ships have  been  shown  to  be  evidences  and  results  of  the  degree 
of  affinity  in  descent  from  common  progenitors,  and  are  revised 
accordingly.  The  definition  of  '  ape,'  for  example,  as  a  'variety  of 
the  quadrumana  having  teeth  like  man,  etc.,'  is  widened  to  include 
less  obvious  characteristics;  and  this  and  other  similarities  to  man, 
which  the  older  definition  merely  stated,  are  now  explained.  In 
all  such  cases,  the  genetic  definition  tells  us  more  about  the  real 
nature  of  the  thing  defined,  because  it  relates  the  thing,  through 
general  laws  of  behaviour,  to  other  things  and  their  characteristics. 
Again,  there  are  other  cases  where  either  mode  of  definition  seems 
equally  adequate  in  itself,  and  we  can  employ  them  indifferently 
according  to  the  purpose  of  the  moment.  In  mathematics,  for 
example,  a  circle  may  be  defined  equally  well  as  '  a  plane  figure 
bounded  by  a  line,  all  points  of  which  are  equally  distant  from  a 
point  within  called  the  centre,' or  as 'the  plane  figure  generated  by 
revolving  a  straight  line  about  one  of  its  extremities  which  remains 
fixed.'  And,  finally,  we  may  mention  a  class  of  genetic  definitions 
whose  value  seems  merely  practical,  in  that  their  purpose  is  only 
to  give  a  brief  statement  of  how  to  make  a  certain  thing  when 
it  is  wanted.  Such  are  the  chemical  formulae  used  in  certain 
manufactures,  or  the  receipts  found  in  cook  books. 

(4)  In  addition  to  the  question  as  to  which  of  these  modes  of 
definition  is  to  be  preferred  in  any  case,  the  further  problem  arises: 
What  are  the  essential  characteristics  which  the  definition  must 
state?  This  also  must  be  determined  by  the  purposes  for  which  it 
is  to  be  used.  The  essential  characteristics  of  any  subject  will  vary 
widely  according  to  the  different  points  of  view  from  which  it  is  ex- 
amined.  The  legal  definition  of  '  insanity,'  for  example,  differs  from 


jS  Definition  and  Division 

the  medical.  Jurisprudence  is  concerned  here  not  with  the  stud) 
of  mental  abnormality  as  such,  but  with  the  determination  of  that 
degree  of  it  which  it  is  expedient  to  recognize  as  constituting  irre- 
sponsibility for  what  would  usually  be  considered  as  a  criminal  act, 
or  as  nullifying  contracts,  deeds,  and  wills.  And,  in  general, 
we  may  say  that  the  purpose  of  definitions  in  law  is  always  to 
insure  that  the  original  intention  of  the  legislator  shall  be  carried 
out,  by  stating  as  clearly  as  possible  the  distinguishing  marks 
of  the  agents,  acts,  or  states  to  which  the  law  is  intended  to  apply. 
This  purpose,  and  not  that  of  an  exact  statement  of  the  nature  of 
the  thing  defined,  determines  what  shall  be  considered  essential 
characteristics  in  its  eyes.  It  is  plain  that  there  may  often  be.  there- 
fore, an  important  difference  between  a  good  legal  definition  and  a 
good  definition  of  the  same  subject-matter  in  one  of  the  natural 
sciences,  for  example.  This  example  will  also  serve  to  illustrate 
the  truth  that  it  is  neither  necessary  nor  desirable  that  all  definitions 
should  be  equally  precise.  A  definition  which,  from  one  point  of 
view,  lacks  logical  completeness  may  sometimes  be  sufficiently  exact 
for  the  purpose  on  hand.  Such  is  the  case,  for  example,  with  those 
definitions  which  are  preliminary  in  any  science  or  argument,  and 
serve  to  outline  its  field  and  to  prepare  the  way  for  further  discussion. 
Too  great  haste  in  defining  is  in  its  way  almost  as  much  a  fault  as 
failure  to  define  at  all;  and  there  is  a  peculiar  fallacy  which  at- 
tempts to  bar  the  way  to  all  fruitful  discussion  by  remarking  that '  it 
is  all  a  question  of  definition,  and  if  the  terms  had  been  first  defined, 
all  this  argument  would  be  unnecessary.'  The  remark  is  perfectly 
true,  but  it  overlooks  the  fact  that  any  fully  adequate  definition  is 
the  product  of  thinking,  not  its  point  of  departure. 

In  the  general  rules  of  definition,  therefore,  the  terms  'genus'  and 
'  specific  differentia  '  should  be  taken  in  a  wide  sense.  It  should  be 
remembered  that  they  vary  with  the  purpose  of  the  definition, 
and  that  that  purpose  may  be  either  merely  to  insure  recognition  by 
the  statement  of  convenient  marks  or  signs,  as  in  the  '  diagnostic ' 


§  ig.   Division  77 

definitions  of  disease  for  the  use  of  the  physician;  or  it  may  be  the 
ordered  arrangement  of  the  subject-matter  of  a  science,  as  sum- 
ming up  the  knowledge  we  already  have  and  stating  it  in  convenient 
form  for  preservation  and  further  investigation ;  or,  again,  it  may 
be  the  concise  statement  of  the  way  in  which  particular  processes 
and  objects  are  explained  by  the  general  laws  of  causation. 
According  to  these  varying  purposes,  both  '  genus '  and  '  specific 
differentia '  may  be  sometimes  descriptive,  sometimes  explicative, 
sometimes  fixed  classes,  sometimes  genetic  processes. 

§  19.  Division.  —  We  have  already  spoken  of  Division  as  a 
process  of  defining  a  term  from  the  point  of  view  of  extension. 
This  is  to  enumerate  the  objects  or  classes  of  objects  which 
the  term  denotes.  This  enumeration  must,  however,  be 
guided  by  certain  principles  which  we  have  now  to  consider. 

It  is  usual  to  begin  this  subject  by  speaking  of  Dichotomy, 
or  the  division  of  a  term  into  two  parts  (St%a  tg^vuv,  to  cut 
in  two).  This  is  a  purely  formal  process,  and  is  based  on  the 
so-called  law  of  Excluded  Middle,  which  is  regarded  as  one  of 
the  fundamental  laws  of  thought.  This  law  may  be  stated  as 
follows:  There  is  no  middle  ground  between  contradictories. 
Any  term,  a,  is  either  &ornot-6.  A  triangle  is  either  equilateral 
or  not-equilateral.  Of  two  contradictory  predicates,  one  or 
the  other  must  belong  to  every  possible  subject. 

Now  it  is  clear  that  this  is  a  purely  formal  principle  of  divi- 
sion. Some  positive  knowledge  of  the  particular  facts  involved 
is  always  necessary,  in  order  to  enable  one  to  determine  what 
things  do  stand  in  this  relation  of  logical  opposition.  The 
logical  law,  in  other  words,  does  not  help  us  at  all  in  deciding 
what  may  be  regarded  as  not-a  in  any  particular  case.  It  is 
not,  therefore,  a  means  of  increasing  our  knowledge,  but 
merely  a  principle  of  order  and  arrangement.    This  fact,  obvi- 


^8  Definition  and  Division 

ous  as  it  seems,  was  not  understood  by  the  Schoolmen  who 
busied  themselves  with  logic  in  the  latter  part  of  the  Middle 
Ages.  They  clung  firmly  to  the  belief  that  it  was  possible  to 
discover  the  nature  of  particular  facts  by  purely  formal  opera- 
tions of  this  kind.  Accordingly,  they  spent  a  great  deal  of 
time  in  classifying  and  arranging  terms  as  contradictories, 
contraries,  etc.  This  work  was  doubtless  of  much  service  in 
fixing  the  meaning  of  terms,  and  in  preventing  confusion 
in  their  employment.  But  it  was  a  purely  verbal  investigation, 
and,  of  course,  could  not  lead  to  any  discoveries  regarding  the 
nature  of  things. 

Moreover,  it  must  be  noticed  that  we  do  not  always  get 
propositions  to  which  any  meaning  can  be  attached  by  uniting 
subjects  and  predicates  in  this  way.  If  the  law  of  dichotomy 
is  not  guided  by  knowledge  of  the  particular  facts,  it  will  give 
absurd  propositions  like  '  virtue  is  either  square  or  not-square,' 
'  iron  is  either  pious  or  not-pious.'  Unmeaning  propositions  of 
this  kind  being  left  out  of  account,  however,  we  may  proceed 
to  divide  everything  according  to  this  principle.  All  geo- 
metrical figures  are  either  rectilinear  or  not-rectilinear;  all 
rectilinear  figures  either  triangular  or  not-triangular;  all 
triangles,  equilateral  or  not-equilateral,  etc.  This  method  of 
division  may  be  represented  thus:  — 

Substance 


Material  non-material 

1 

I 1      . 

Organic  not-organic 

I 1 

Mineral  not -mineral 

I 

1 1 

Gold  not-gold 


§  19.   Division  79 

If  it  were  desirable,  the  terms  'non-material,'  'organic/  and 
1  not-mineral '  might  also  be  further  subdivided  in  the  same 
way. 

Now  it  is  not  difficult  to  see  that  the  practical  use  of  this 
principle  will  depend  upon  our  ability  to  find  some  positive 
value  for  the  negative  not-a.  That  is,  to  make  the  law  of  more 
than  formal  value,  we  must  know  what  concrete  term  excludes 
a,  or  is  its  logical  contradictory.  And  knowledge  of  this  kind 
comes,  as  already  said,  only  from  experience  of  the  par- 
ticular facts.  The  strictly  logical  contradictory  of  a  is  always 
not-a;  of  wise,  not-wise;  of  cold,  not-cold;  etc.  Mistakes 
frequently  arise  in  stating  contradictories  in  a  positive  form. 
The  difficulty  is  that  terms  are  chosen  which  are  not  true 
logical  contradictories.  Thus,  if  we  say  that  every  man  is 
either  wise  or  foolish,  our  terms  are  not  contradictories,  for  a 
middle  ground  between  them  is  possible.  The  same  would  be 
true  of  divisions  like  '  large  or  small,'  '  rich  or  poor,'  '  saint  or 
sinner,'  '  idle  or  diligent.'  In  general,  it  is  safe  to  scrutinize 
all  dichotomic  divisions  very  sharply,  to  see  that  the  alterna- 
tives are  really  contradictories. 

The  method  of  dichotomy  depends,  as  we  have  seen,  upon 
the  law  of  Excluded  Middle.  But  there  is  also  another  pro- 
cess called  Division  in  logic,  which  is  perhaps  better  known  by 
its  less  technical  name  of  Classification.  In  classification, 
there  is  no  necessary  limit  to  the  number  of  classes  or  divisions 
which  may  be  obtained.  In  this  respect,  it,  of  course,  differs 
fundamentally  from  the  twofold  division  which  we  have  been 
examining.  Furthermore,  a  classification  is  always  made 
according  to  some  principle  which  is  retained  throughout 
the  whole  process.  Any  common  characteristic  of  the  group 
of  individuals  to  be  divided  may  be  taken  as  a  principle  of 


So  Definition  and  Division 

classification.  If,  however,  the  characteristic  chosen  is 
merely  an  external  and  accidental  one,  the  classification 
based  upon  it  will  be  regarded  as  artificial,  and  made  for 
some  special  or  temporary  purposes.  Thus  we  might  divide 
all  flowering  plants  according  to  the  colour  of  the  flowers,  or 
the  persons  in  any  company  according  to  the  pattern  of  their 
shoes.  A  classification  which  proceeds  upon  such  surface 
distinctions  has,  of  course,  no  real  or  scientific  value,  except 
as  it  aids  us  to  discover  more  fundamental  or  deep-lying  re- 
semblances between  the  individuals  with  which  it  deals,  of 
which  we  may  regard  these  superficial  qualities  as  signs. 
Such  a  preliminary  classification  corresponds  to  what  we 
Ziave  called  the  '  diagnostic  '   definition  (§  18). 

A  scientific  or  natural  classification,  on  the  other  hand,  has 
for  its  purpose  the  statement  of  real  likeness  or  resemblance. 
It  seeks  to  find  and  group  together  the  things  which  are  related 
in  some  essential  point.  Consequently,  it  selects  as  its  princi- 
ple of  division  some  property  which  appears  to  be  a  real  mark 
of  individuality,  and  to  be  connected  with  changes  in  other 
properties.  Such  a  real  principle  of  natural  classification  is 
rarely  found  by  comparison  of  merely  one  property  or  set  of 
properties  in  the  things  to  be  compared.  To  classify  accord- 
ing to  a  single  property  may  be  a  convenient  method  of  giving 
names  to  any  group  of  individuals,  and  of  arranging  them  in 
such  a  way  as  to  be  useful  to  the  student.  It  does  not,  how- 
ever, give  any  adequate  idea  of  the  properties  and  true  rela- 
tions of  the  individuals  compared.  A  really  scientific,  or 
natural,  classification  must  be  based  upon  a  study  and  com- 
parison of  all  the  discoverable  properties  of  the  different  in- 
dividuals to  be  classified.  It  is  only  in  this  way  that  their 
real  resemblance  and  affinities  can  be  brought  to  light. 


§  ig.   Division  81 

The  classification  of  plants  proposed  by  the  famous  Swedish  bot- 
anist, Karl  Linnaeus  (1707-1778),  was  based  upon  the  comparison  of 
a  single  feature :  the  structure  of  the  sexual  organs  of  plants.  This 
method  proved  of  the  greatest  convenience  in  indexing  plants  in  a 
convenient  way  into  genera  and  species  so  that  they  could  be  named 
and  described.  Yet  since  the  classification  adopted  was  based  upon 
a  single  property  or  feature  of  the  plant,  it  was  considered  (even  by 
Linnaeus  himself)  as  merely  artificial.  Of  course  it  is  not  so  obvi- 
ously artificial  as  the  examples  of  what  we  may  perhaps  call  merely 
accidental  or  trivial  classification  given  above.  But  Linnaeus's 
system  did  not  aim  at  setting  forth  the  true  relations  of  plants,  and  it 
was  not  based  upon  any  systematic  study  of  all  their  properties.  It 
is  useful  merely  as  a  stepping-stone  to  the  real  study  of  plants  which 
is  presupposed  in  natural  classification. 

Certain  rules  for  division  are  usually  given  in  connection 
with  the  treatment  of  this  subject.  It  is  not,  of  course, 
supposed  that  by  their  help  one  can  properly  divide  any 
subject  without  special  knowledge.  The  purpose  of  these 
rules  is  rather  to  warn  against  the  logical  errors  to  which 
one  is  most  liable  in  the  process  of  division. 

(1)  Every  division  is  made  on  the  ground  of  differences 
appearing  in  the  fundamental  nature  which  is  common  to 
all  the  members  of  the  whole  to  be  divided. 

(2)  Every  division  must  be  based  on  a  single  principle 
or  ground  {fundamenlum  divisionis). 

(3)  The  constituent  species  (or  groups  into  which  the 
whole  is  divided)  must  not  overlap,  but  must  be  mutually 
exclusive. 

(4)  The  division  must  be  exhaustive,  i.e.  the  constituent 
species  must  be  equal,  when  added  together,  to  the  genus. 

The  first  rule  requires  no  remark.     It  simply  states  that 

G 


82  Definition  and  Division 

it  is  only  possible  to  divide  any  whole  on  the  basis  of  differ- 
ences  in  something  which  is  common  to  all  its  parts.  The 
second  rule  warns  against  changing  the  principle  of  division 
while  the  process  is  being  carried  out.  This  law  would  be 
violated,  if,  for  example,  one  were  to  divide  mankind  into 
Caucasians,  Negroes,  Mongolians,  Europeans,  Australians, 
and  Americans.  The  principle  of  division  which  was  first 
adopted  in  this  example  was  obviously  that  of  the  colour  of 
the  skin.  But  this  principle  was  not  carried  through,  and 
another  principle,  that  of  geographical  distribution,  was 
substituted  for  it.  In  dividing  one  must  be  clearly  conscious 
of  the  principle  which  one  is  using,  and  keep  a  firm  hold  of 
it  until  the  division  is  completed.  The  example  which  we 
have  just  given  also  violates  the  third  rule.  For  not  all  of 
the  groups,  European,  Caucasian,  etc.,  exclude  one  another. 
Similarly,  it  would  not  be  good  logic  to  divide  animals 
into  vertebrates,  mammals,  insects,  birds,  mollusks,  and  fishes. 
The  fourth  rule  simply  insists  that  the  division  must  be 
complete.  The  whole  must  be  completely  included  in  its 
divisions.  It  would  not  be  a  complete  division  to  say  that 
books  may  be  divided  into  folios,  quartos,  and  duodecimos, 
or  vertebrates  into  mammals  and  birds.  For  in  neither 
of  these  examples  are  the  divisions  enumerated  equal  to  the 
whole  class. 

We  have  discussed  Division  as  though  it  always  proceeded  from 
the  whole  to  its  parts,  from  the  genus  to  its  species.  But  the  con- 
trary procedure  is  quite  as  frequent,  and  in  the  natural  sciences  is 
the  method  more  usually  followed.  In  this  we  start  with  a  more  or 
less  miscellaneous  assemblage  of  objects,  examine  and  compare 
them,  and  gradually  arrange  them  into  groups  on  the  basis  of  the 
observed  likenesses  and  differences.     These  groups  may  again  be 


§  19.    Division  83 

assembled  into  more  inclusive  groups  in  the  same  way,  and  the 
process  continued  until  we  have  a  systematic  classification  of 
the  collection  with  which  we  began.  The  name  of  Classification  is 
often  reserved  for  this  procedure,  Division  being  applied  only  to 
the  method  already  described.  As  a  matter  of  fact,  however,  this 
distinction  seems  to  be  merely  relative.  Even  classification  in  this 
narrower  sense  presupposes  some  vague  idea  of  the  whole,  which 
enables  us  to  mark  off  in  a  preliminary  way  the  objects  to  be 
classified  from  other  objects ;  otherwise  its  task  would  be  infinite. 
And  it  is  perhaps  more  usual  than  not  that  we  classify  in  both 
ways  at  the  same  time.  To  borrow  an  illustration  from  Mr. 
Joseph,  'if  one  were  asked  to  divide  the  genus  "novel,"  he  might 
suggest  a  division  into  the  novel  of  adventure,  of  character,  and  of 
plot;  but  he  would  at  the  same  time  run  over  in  thought  the 
novels  he  had  read,  and  ask  himself  if  they  could  be  classed  satis- 
factorily under  these  three  heads.'  Division,  in  fact,  in  any  of  its 
forms,  presupposes  and  involves  definition.  Now  definition,  as 
we  have  already  seen,  is  based  on  induction,  or  an  examination 
of  the  particular  things  to  be  defined ;  and  whether  we  first  notice 
their  general  likeness  one  to  another,  or  the  special  differences 
that  exist  between  them  along  with  this  likeness,  is  largely  a 
matter  of  accident,  or  is  determined  by  the  special  purpose  of 
the  investigation. 

REFERENCES 

J.  S.  Mill,  Logic,  Bk.  L,  Chs.  VII.  and  VIII. 

W.  Minto,  Logic  Inductive  and  Deductive,  Pt.  II.,  pp.  82-130. 

C.  Sigwart,  Logic,  Vol.  I.,  §§  42-44- 

J.  H.  Hyslop,  The  Elements  of  Logic,  Ch.  VI. 

H.  Rickert,  Zur  Lehre  von  der  Definition. 


CHAPTER  VI 

PROPOSITIONS 

§  20.  The  Nature  of  a  Proposition.  —  A  proposition  is 
the  expression  in  words  of  an  act  of  judgment.  It  is  com- 
posed, as  we  have  already  seen,  of  two  terms,  a  subject 
and  a  predicate,  connected  by  a  copula.  From  the  point 
of  view  of  formal  logic  the  predicate  is  affirmed  (or  denied) 
of  the  subject.  When  we  come  to  consider  the  nature  of 
judgment  (cf.  especially  §§  78,  81),  we  shall  find  reasons 
for  questioning  whether  this  analysis  of  the  proposition  can 
be  regarded  as  furnishing  a  correct  account  of  what  actually 
takes  place  in  judgment.  When  we  judge,  we  do  not  begin 
with  words  or  terms  which  are  not  yet  judgments,  and  then 
pass  on  to  judgment  by  joining  the  former  together  in  an 
external  way.  The  conclusions  which  we  shall  have  to  adopt 
are,  that  terms  represent  ways  of  judging,  that  the  simplest 
act  of  thought  is  already  a  judgment,  and  that  thinking 
develops  by  advancing  from  incomplete  to  more  complete 
and  comprehensive  judgments.  The  theory  of  the  syllo- 
gism is,  however,  worked  out  on  the  view  that  the  proposi- 
tion expresses  a  relation  between  subject  and  predicate. 
This  is  sufficiently  accurate  for  practical  purposes,  and  is 
not  likely  to  lead  to  any  serious  mistakes  so  long  as  we 
remember  that  it  is  the  proposition,  rather  than  the  actual 
nature  of  judgment,  with  which  we  are  dealing 

The  logical  proposition,  as  the  expression  of  an  act  of 

84 


§  20.    The  Nature  of  a  Proposition  85 

thought,  corresponds  to  the  grammatical  sentence.  Not 
every  sentence,  however,  is  a  logical  proposition.  Sen- 
tences which  express  a  wish  or  an  interrogation  do  not 
directly  enter  into  the  process  of  argument  at  all,  and  may 
therefore  be  neglected  for  the  present.  The  same  is  true 
of  exclamatory  sentences.  Again,  even  indicative  sen- 
tences frequently  require  to  be  rewritten  in  order  to  reduce 
them  to  the  form  of  a  logical  proposition,  which  demands 
two  terms  and  a  copula.  The  sentence,  '  the  sun  shines,' 
must,  therefore,  for  purposes  of  logical  treatment,  be  reduced 
to,  '  the  sun  is  a  body  which  shines.'  '  On  the  hillside 
deep  lies  the  snow,'  is  expressed  as  a  logical  proposition 
in  some  such  form  as  this:  'The  snow  is  a  covering  lying 
deep  on  the  hillside.'  It  is  very  important  to  change  the 
grammatical  sentence  to  the  regular  form  of  a  proposition 
before  attempting  to  treat  it  logically. 

The  most  general  division  of  propositions  is  that  which 
classifies  them  as  Categorical  and  Conditional.  A  categorical 
proposition  asserts  directly,  and  without  any  condition. 
The  predicate  is  either  affirmed  or  denied  unconditionally 
of  the  subject.  '  A  is  B,' '  this  room  is  not  cold,'  '  New  York 
is  the  largest  city  in  America,'  are  examples  of  categorical 
propositions.  Conditional  propositions,  on  the  other  hand, 
state  the  consequences  which  necessarily  follow  from  a 
supposition,  or  hypothesis,  and  do  not  directly  assert  any- 
thing about  particular  matters  of  fact;  as,  e.g.,  *  we  shall  go 
to-morrow,  if  it  does  not  rain.'  '  It  will  either  rain  or  snow 
to-morrow,'  is  also  a  conditional  proposition;  for  neither 
rain  nor  snow  are  asserted  directly  and  absolutely,  but  in 
each  case  the  appearance  of  the  one  is  dependent  upon  the 
non-appearance  of  the  other. 


86  Propositions 

The  first  of  these  conditional  propositions  is  known  as 
a  Hypothetical,  and  the  latter  as  a  Disjunctive  proposition; 
but  for  the  present  we  shall  deal  only  with  categorical  propo- 
sitions, and  with  the  form  of  syllogistic  argument  to  which 
they  give  rise.  After  we  have  completed  the  account  of  the 
categorical  syllogism,  however,  it  will  be  necessary  to  return 
to  a  consideration  of  conditional  propositions,  and  to  the 
class  of  arguments  in  which  they  are  employed. 

§  21.  The  Quality  and  Quantity  of  Propositions.  —  We 
shall  now  consider  the  various  kinds  of  categorical  proposi- 
tions. Such  propositions  are  classified  with  regard  to 
Quality  and  Quantity.  From  the  standpoint  of  quality, 
propositions  are  either  Affirmative  or  Negative.  -An  affirma- 
tive proposition  is  one  in  which  an  agreement  is  affirmed 
between  the  subject  and  predicate,  or  in  which  the  predicate 
is  asserted  of  the  subject.  The  proposition,  '  snow  is  white,' 
for  example,  indicates  such  an  agreement  between  the  sub- 
ject and  predicate,  and  is  therefore  affirmative  in  quality. 
A  negative  proposition  indicates  a  lack  of  agreement  or  har- 
mony between  the  subject  and  predicate.  The  predicate  does 
not  belong  to  the  subject,  but  all  relation  or  connection  be- 
tween the  two  is  denied.  'The  room  is  not  cold,'  '  the  trees 
are  not  yet  in  full  leaf,'  are  examples  of  negative  propositions. 

The  Quantity  of  a  proposition  is  determined  by  the  exten- 
sion of  the  subject.  When  the  proposition  refers  to  all  of 
the  individuals  denoted  by  the  subject,  it  is  said  to  be  Uni- 
versal in  quantity.  When,  on  the  other  hand,  the  propo- 
sition affirms  that  the  predicate  belongs  only  to  a  part  of  the 
subject,  it  is  said  to  be  Particular.  For  example,  '  all  metals 
are  elements'  is  a  universal  proposition,  because  the  assertion 
is  made  of  the  subject  in  its  widest  or  fullest  extent;   'some 


§  21.    T/ie  Quality  and  Quantity  of  Propositions     87 

metals  are  white'  is  a  particular  proposition,  because  refer- 
ence is  made  to  only  a  part  of  the  subject  '  metal.' 

We  divide  propositions,  then,  with  regard  to  quantity, 
into  Universal  and  Particular  propositions.  Universal  propo- 
sitions are  often  indicated  by  adjectives  like  'all,'  'the  whole,' 
'every,'  etc.  It  frequently  happens,  however,  that  no  such 
mark  of  universality  is  present.  A  scientific  law  is  usually 
stated  without  any  explicit  statement  of  its  quantity,  though 
from  its  very  nature  it  is  meant  to  be  universal.  Thus  we 
say,  '  the  planets  revolve  around  the  sun,'  'comets  are  subject 
to  the  law  of  gravitation.'  Propositions  which  have  a  singu- 
lar or  an  individual  name  as  subject  are  often  called  Indi- 
vidual propositions,  as,  e.g.,  'the  earth  is  a  planet,'  'know- 
ledge is  power.'  But  since  it  is  impossible  to  limit  a  singular 
subject,  individual  propositions  are  to  be  regarded  as  univer- 
sal. They  belong,  that  is,  to  the  class  of  propositions  which 
employ  the  subject  term  in  its  complete  extent. 

Another  class,  called  Indefinite  or  Indesignate  propo- 
sitions, has  sometimes  been  proposed.  This  class  is  usually 
said  to  include  propositions  in  which  the  form  of  the  words 
does  not  give  any  indication  whether  the  predicate  is  used 
of  the  whole,  or  only  of  a  part  of  the  subject.  'Men  are  to 
be  trusted,'  'animals  are  capable  of  self-movement,'  may 
serve  as  examples.  This  classification  may  be  useful  in 
illustrating  the  evil  of  making  indefinite  or  ambiguous 
statements.  Otherwise  there  is  nothing  to  be  learned  from 
it.  A  really  indefinite  proposition  has  no  place  in  an  argu- 
ment, and  logic  rightfully  refuses  to  deal  with  it.  The  first 
demand  of  logic  is  that  our  statements  shall  be  clear  and 
precise.  A  proposition  is  not  necessarily  indefinite,  how- 
ever, because  it  has  no  qualifying  words  like  '  all '  or '  some.' 


88  Propositions 

It  is  the  meaning  of  a  proposition  as  a  whole,  rather  than  the 
form  of  its  subject,  which  renders  it  definite  or  indefinite 
Where,  on  the  other  hand,  it  is  really  impossible  to  decide 
whether  the  proposition  is  universal  or  particular,  logic 
forbids  us  to  proceed  with  the  argument  until  this  point 
has  been  made  clear. 

Particular  propositions  are  usually  preceded  by  some 
word  or  phrase  which  shows  that  the  subject  is  limited 
in  the  extent  of  its  application.  The  logical  sign  of  particu- 
lar propositions  is  'some,'  but  other  qualifying  words  and 
phrases,  such  as  'the  greatest  part,'  'nearly  all,'  'several,' 
'a  small  number,'  etc.,  also  indicate  particularity.  Here 
again,  however,  it  is  the  meaning  of  the  proposition,  rather 
than  its  form,  which  is  to  be  considered.  'All  metals  are 
not  white,'  for  example,  is  a  particular  proposition,  although 
introduced  by  'all,'  since  it  is  clearly  equivalent  to  'some 
metals  are  not  white.'  '  Every  mark  of  weakness  is  not  a 
disgrace,'  again,  is  a  particular  proposition,  and  signifies 
that  'not  all,  or  some  marks  of  weakness  are  not  disgraceful.' 

The  words  'few'  and  'a  few'  require  special  attention. 
The  latter,  as  in  the  proposition,  '  a  few  persons  have  spoken 
to  me  about  it,'  is  equivalent  to  'some,'  and  introduces  a 
particular  affirmative  proposition.  'Few,'  on  the  other 
hand,  is  negative  in  character.  Thus,  'few  were  saved  from 
the  shipwreck'  implies  that  only  a  few  were  saved,  or  that 
the  greater  number  did  not  escape,  and  the  proposition  is 
therefore  to  be  considered  as  a  particular  negative. 

Propositions,  then,  are  classified  as  affirmative  and  nega- 
tive in  Quality,  universal  and  particular  in  Quantity.  When 
these  classifications  are  combined,  we  get  four  kinds  of 
propositions,  to  symbolize  which  the  vowels  A,  E,  I,  O  are 


§  22.    Difficulties  in  Classification  89 

employed.  A  and  I,  the  vowels  contained  in  afjirmo,  stand  for 
affirmative  propositions;  E  and  O,  the  vowels  in  nego,  for  neg- 
ative propositions.    This  may  be  represented  as  follows: — ■ 

,  f  Affirmative:  All  S  is  P.  A 

Universal  ^    T       .  XT    „  .    _  _ 

I  Negative :      No  S  is  P.  E 

.     ,      [Affirmative:   Some  S  is  P.  I 

Particular  \  . 

1  Negative :       Some  S  is  not  P.  U 

We  shall  henceforth  use  A,  E,  I,  and  O  to  represent  respec- 
tively a  universal  affirmative,  a  universal  negative,  a  particu- 
lar affirmative,  and  a  particular  negative  proposition.  In 
dealing  with  propositions  logically,  the  first  step  is  to  reduce 
them  to  one  or  other  of  these  four  types.  This  can  be 
accomplished  readily  by  noticing  the  distinctions  previously 
laid  down.  There  are,  however,  certain  grammatical 
forms  and  sentences  which  present  some  difficulty,  and  it 
may  therefore  be  useful  to  consider  them  separately. 

§22.  Difficulties  in  Classification.  —  In  the  first  place, 
we  may  notice  that  in  ordinary  language  the  terms  of  a 
proposition  are  frequently  inverted,  or  its  parts  separated 
in  such  a  way  that  it  requires  attention  to  determine  its  true 
logical  order.  In  the  proposition,  'now  came  still  evening 
on,'  for  example,  the  subject  'still  evening'  stands  between 
two  portions  of  the  predicate.  As  a  logical  proposition,  the 
sentence  would  have  to  be  expressed  in  some  such  form  as 
the  following:  '  Still  evening  is  the  time  which  now  came  on.' 
Similarly,  we  should  have  to  write  an  inverted  sentence 
like,  'deep  lies  the  snow  on  the  mountain,'  as  'the  snow  is 
something  which  lies  deep  on  the  mountain.' 

If  a  subject  is  qualified  by  a  relative  clause,  the  verb  of  the 
latter  must  not  be  confused  with  the  main  assertion  of  the 
proposition.  Take  the  sentence,  'he  is  brave  who  conquers  his 


po  Propositions 

passions.'  Here  it  is  evident  that  the  relative  clause  describes 
or  qualifies  'he.'  Logically,  then,  the  proposition  is  of  the  form 
A,  and  is  to  be  written, '  he  who  conquers  his  passions  is  brave.' 
The  reader  will  notice  that  all  propositions  which  begin  with 
pronouns  like  '  he  who,' '  whoever,'  etc.,  are  universal  in  quan- 
tity, since  they  mean  all  who  belong  to  the  class  in  question. 

(i)  We  have  reduced  grammatical  sentences  to  logical  propo- 
sitions by  changing  the  form  in  such  a  way  as  to  have  two  terms 
united  by  'is'  or  '  are '  as  the  copula.  Such  a  proposition,  however, 
does  not  express  time,  but  simply  the  relation  existing  between 
subject  and  predicate.  When  the  grammatical  sentence  does 
involve  a  reference  to  time,  and  especially  to  past  or  future  time, 
the  reduction  to  logical  form  is  somewhat  awkward.  Perhaps  the 
best  method  is  to  throw  the  verb  expressing  time  into  the  predi- 
cate. Thus  'the  steamer  will  sail  to-morrow'  =  'the  steamer  is  a 
vessel  which  will  sail  to-morrow ' ;  'we  waited  for  you  two  hours  yes- 
terday '  =  '  we  are  persons  who  waited  for  you  two  hours  yesterday. ' 

(2)  Exclusive  propositions  exclude  all  individuals  or  classes 
except  those  mentioned  by  the  use  of  some  such  word  as  'except,' 
'none  but,'  'only.'  'None  but  the  guilty  fear  the  judge';  'only 
citizens  can  hold  property';  'no  admittance  except  on  business.' 
These  propositions  may  all  be  reduced  to  the  form  E  by  writing 
'  no '  before  the  contradictory  of  the  subject  term.  Thus  '  none  but 
the  guilty  fear  the  judge'  =  'no  one  who  is  not  guilty  fears  the 
judge';  'only  citizens  can  hold  property'  =  'no  one  who  is  not  a 
citizen,  etc.';  'no  admittance  except  on  business'  =  'no  person 
who  has  not  business  is  to  be  admitted.'  Or,  by  taking  the  predi- 
cate as  subject,  the  meaning  of  the  proposition  may  be  expressed 
affirmatively:  'all  who  fear  the  judge  are  guilty';  'all  who  can 
hold  property  are  citizens.' 

§  23.  Formal  Relation  of  Subject  and  Predicate.  —  We 
have  now  to  consider  how  the  relation  existing  between 


§  23.    Formal  Relation  of  Subject  and  Predicate     91 

the  terms  of  a  proposition  is  to  be  understood.     In  §  16  it  was 
shown  that  every  term  may  be  interpreted  in  two  ways :  either 
from  the  point  of  view  of  extension,  or  from  that  of  intension. 
Extensively,  terms  are  taken  to  represent  objects  or  classes  of 
objects;  while  their  meaning  in  intension  has  reference  to  the 
attributes  or  qualities  of  things.    Now  the  interpretation  of  the 
categorical  proposition  given  by  formal  logic  is  based  entirely 
on  extension.    That  is,  the  subject  and  predicate  are  regarded 
as  standing  for  individual  objects  or  classes  of  objects.    The 
question  to  be  considered,  then,  concerns  the  extensive  relation 
of  these  groups  of  objects  in  the  propositions  A,  E,  I,  andO. 
This  mode  of  interpreting  propositions  must  not  be  taken 
as  furnishing  an  adequate  theory  of  the  nature  of  the  act  of 
judgment  which  is  expressed  in  the  proposition.     It  leaves 
entirely  out  of    account  the  intensive  meaning,  or  the  con- 
nection  of   attributes   asserted   by   the   proposition,    which 
in  many  cases  is  the  most  prominent  part  of  its  signification. 
Thus  the  proposition,  '  all  metals  are  elements,'  implies  that 
the  quality  of  being  an  element  is  united  with  the  other 
qualities  connoted  by  the  term  '  metal.'     Indeed,  this  inter- 
pretation is  perhaps  more  natural  than  the  one  given  by 
formal  logic,  namely,  that  the  class  of  metals  is  included  in 
the  class  of  elements.     It  must  be  admitted  that  the  extensive 
way  of  reading  propositions,   as  affirming  or  denying  the 
inclusion  of  one  class  of  objects  in  another  class,  frequently 
seems  artificial.     Nevertheless,  it  is  the  view  upon  which 
the  historical  account  of  the  syllogism  is  founded.     And  the 
fact  that  this  mode  of  representing  the  meaning  of  proposi- 
tions leads  in  practice  to  correct  conclusions  proves  that  it  is 
not  wholly  false.     It  represents,  as  we  have  seen  in  discussing 
terms  (§  16), one  side  or  aspect  of  the  meaning  of  propositions. 


92  Propositions 

From  the  point  of  view  of  formal  logic,  then,  a  logical 
proposition  signifies  that  a  certain  relation  exists  between 
the  class  of  things  denoted  by  the  subject,  and  that  denoted 
by  the  predicate.  This  relation  may  be  one  of  inclusion  or 
of  exclusion.  For  example,  the  proposition  <  all  good  men 
are  charitable,'  is  interpreted  to  mean  that  'good  men'  are 
included  in  the  class  of  '  charitable  men.'  On  the  other 
hand,  'no  birds  are  mammals,'  signifies  that  the  two  classes, 
'  birds  '  and  '  mammals,'  are  mutually  exclusive.    The  mean- 


FlG.    I. 

ings  of  the  four  logical  propositions  A,  E,  I,  and  O  may  be 
represented  by  means  of  a  series  of  diagrams,  which  were 
first  used  by  the  celebrated  German  mathematician  Euler, 
who  lived  in  the  eighteenth  century. 

To  represent  the  meaning  of  a  proposition  in  A,  like '  all  good 
men  are  charitable,'  we  draw  a  circle  to  symbolize  the  class  of 
charitable  beings,  and  then  place  inside  it  a  smaller  circle  to 
stand  for  good  men.  The  proposition,  that  is,  signifies  that 
'  good  men '  are  included  in  the  class  of  '  charitable  beings.' 
The  subject  belongs  to,  or  falls  within,  the  larger  class  of 
objects  represented  by  the  predicate. 

It  must  be  carefully  noted  that  proposition  A  does  not  usu- 
ally assert  anything  of  the  whole  of  its  predicate.     In  the  ex- 


§  23.    Formal  Relation  of  Subject  and  Predicate    93 

ample  just  given,  no  assertion  is  made  regarding  the  whole 
class  of  '  charitable  beings,'  but  only  in  so  far  as  they  are 
identical  with  'good  men.'  There  may  possibly  be  other 
charitable  beings  who  are  not  good  men,  or  not  men  at  all. 
The  meaning  of  the  proposition,  then,  is  that  '  all  good  men 
are  some  charitable  beings.'  In  other  words,  the  predicate 
of  the  ordinary  universal  affirmative  proposition  is  taken 
only  in  a  partial,  or  limited  extent:  nothing  is  affirmed  of 
the  whole  of  the  circle  of  charitable  beings.  We  denote 
this  fact  by  saying  that  the  predicate  of  proposition  A  is 
undistributed I.  The  subject,  on  the  other  hand,  as  a  universal 
term,  is  employed  in  its  fullest  extent,  or  is  distributed. 

In  some  cases,  however,  the  predicate  is  not  a  broader 
term  which  includes  the  subject,  but  the  two  are  equal  in 
extent.  In  the  proposition,  '  all  equilateral  triangles  are 
equiangular,'  for  example,  this  is  the  case.  If  we  were 
to  represent  this  proposition  graphically,  the  circle  of  equi- 
lateral triangles  would  not  fall  inside  that  of  equiangular 
triangles,  but  would  coincide  with  it.  The  same  relation 
between  subject  and  predicate  holds  in  the  case  of  log- 
ical definitions.  For  example,  in  the  definition,  '  mon- 
archy is  a  form  of  political  government  where  one  man 
is  sovereign,'  the  subject  is  coextensive  with  the  whole 
of  the  predicate.  In  examples  of  this  kind,  it  is  of  course 
obvious  that  th.e  predicate,  as  well  as  the  subject,  is  distributed. 

As  an  example  of  proposition  E,  we  may  take  the  example, 
'  no  birds  are  mammals.'  The  meaning  of  this  proposition  is 
represented  graphically  by  means  of  two  circles  falling  out- 
side each  other  as  in  Fig.  2. 

The  proposition  asserts  that  the  class  of  birds  falls  com- 
pletely without  the  class  of  mammals,  that  the  two  classes 


94  Propositions 

are  entirely  distinct,  and  mutually  exclusive.  With  regard 
to  quantity,  the  subject  is  of  course  universal  or  distributed. 
And,  in  this  case,  the  predicate  is  also  distributed.  For  the 
proposition  asserts  that  the  subject '  birds  '  does  not  agree  with 
any  part  of  '  mammals.'  Or,  in  terms  of  the  diagram,  we  deny 
that  the  circle  representing   '  birds '   corresponds  with  any 


Fig.  2. 

portion  of  the  circle  '  mammals.'  But  to  exclude  the  former 
circle  completely  from  the  circle  which  represents  '  mammals,' 
it  is  necessary  that  we  know  the  whole  extent  of  the  latter. 
Otherwise  we  could  not  be  sure  that  the  subject  had  not  some 
point  in  common  with  it.  Proposition  E,  therefore,  distributes, 
or  uses  in  their  widest  extent,  both  subject  and  predicate. 

The  meaning  of  a  proposition  in  I,  as,  e.g., '  some  birds  are 
web-footed,'  is  shown  by  means  of  two  circles  intersecting  or 
overlapping  as  in  Fig.  3.  A  part  of  the  class  of  birds  corre- 
sponds with  a  part  of  web-footed  animals.  The  proposition 
has  reference  to  the  common  segment  of  the  two  circles,  which 
may  be  large  or  small.  The  two  circles  correspond  in  part  at 
least.  In  proposition  I,  both  subject  and  predicate  are  undis- 
tributed. The  subject  is,  of  course,  a  particular  or  limited 
term.  And,  as  will  be  clear  from  what  has  already  been  said 
in  the  case  of  proposition  A,  reference  is  made  only  to  a 
limited  portion  of  the  predicate,     in  the  example  used,  the 


§  23.    Formal  Relation  of  Subject  and  Predicate     95 

assertion  refers  only  to  those  web-footed  animals  which  are 
also  birds.  Or  we  may  say  that  the  proposition  has  reference 
only  to  the  common  segment  of  the  circles  representing  sub- 


FlG.  3. 

ject  and  predicate.  Nothing  is  asserted  of  the  other  portions 
of  the  two  circles.  In  other  words,  both  subject  and  predicate 
are  employed  in  a  limited  extent,  or  are  undistributed. 

'  Some  metals  are  not  white,'  may  serve  as  an  example  of 
proposition  O. 

This  proposition  may  be  represented  graphically  as  in 
Fig.  4.      Though  this  is  the  same  form  of  diagram  as  that 


Fig. 


employed  in  the  last  figure,  the  proposition  refers  now  to  the 
outlying  part  of  the  circle  '  metal.'     Some  metals,  it  asserts 


0  Propositions 

do  not  fall  within  the  sphere  of  white  substances.  A  larger  or 
smaller  section  of  the  circle  representing  the  former  term,  falls 
completely  without  the  circle  of  white  substances. 

It  is  necessary  to  notice  carefully  that  although  the  subject 
of  O  is  undistributed,  its  predicate  is  distributed.  Fcr,  as  we 
have  seen,  a  part  of  the  subject  is  completely  excluded  from 
the  class  of  'white substances.'  But  in  order  to  exclude  from 
every  part  of  the  predicate,  the  full  extent  of  the  predicate  must 
be  known.  Or,  in  terms  of  the  diagram,  the  proposition  ex- 
cludes a  portion  of  the  circle  of  metals  (some  metals)  from 
each  and  every  part  of  the  circle  of  white  things.  The  latter 
term  must  therefore  be  used  in  its  full  extent,  or  be  distributed. 

It  is  absolutely  necessary,  in  order  to  comprehend  what 
follows,  to  understand  the  distribution  of  terms  in  various 
propositions.  It  may  help  the  reader  to  remember  this  if 
we  summarize  our  results  in  the  following  way:  — 

Proposition  A,  subject  distributed,  predicate  undistributed. 
Proposition  E,  subject  distributed,  predicate  distributed. 
Proposition  I,  subject  undistributed,  predicate  undistributed. 
Proposition  O,  subject  undistributed,  predicate  distributed. 

REFERENCES  TO    §23 

J.  N.  Keynes,  Studies  and  Exercises  in  Formal  Logic,  Part  II.,  Chs.  I 
and  II. 

J.  S.  Mill,  Logic,  Bk.  I.,  Ch.  V. 

C.  Sigwart,  Logic,  §5. 

B.  Bosanquet,  The  Essentials  of  Logic,  Lectures  V.  and  VI. 


CHAPTER    VII 

THE    INTERPRETATION   OF   PROPOSITIONS 

§  24.   The  So-called  Process  of    Immediate  Inference.  — 

Many  logicians  speak  of  two  kinds,  or  processes  of  reasoning, 
to  which  they  give  the  names  of  Mediate,  and  Immediate 
inference.  Mediate  inference,  it  is  said,  asserts  the  agree- 
ment or  disagreement  of  a  subject  and  predicate  after  hav- 
ing compared  each  with  some  common  element  or  middle 
term.  The  conclusion  is  thus  reached  mediately  or  indirectly. 
The  syllogism  is  the  best  example  of  mediate  inference.     In 

the  syllogism, 

All  M  is  P, 
All  S  is  M, 
Therefore  S  is  P, 

the  conclusion  is  reached  through  the  medium  of  M,  with 
which  both  S  and  P  have  been  compared.  It  will  be  noticed 
that  to  obtain  a  conclusion  in  this  way  two  propositions  or 
premises  are  necessary. 

We  sometimes  are  able,  however,  to  pass  directly  or  imme- 
diately from  one  proposition  to  another.  For  example,  the 
proposition  that '  no  men  are  infallible,'  warrants  the  statement 
that  '  no  infallible  beings  are  men.'  Or,  if  we  know  that  it  is 
true  that  'some  birds  are  web-footed,'  we  perceive  at  once  that 
the  proposition,  '  no  birds  are  web-footed,'  is  false.  It  is  this 
k  97 


98  The  Interpretation  of  Propositions 

process  of  passing  directly  from  one  proposition  to  another 
which  has  been  named  by  many  logicians  Immediate  infer- 
ence. 

The  question  may  be  raised,  however,  whether  the  direct 
passage  from  one  proposition  to  another,  as  in  the  above 
examples,  should  properly  be  called  inference,  or  whether 
the  change  is  not  merely  in  the  verbal  expression.  As  we 
have  already  shown,  inference  is  a  process  of  exhibiting  the 
relation  of  facts  to  one  another  by  discovering  some  common 
element  or  connecting  principle  by  means  of  which  they  are 
united  (cf.  also  §  92).  Wherever  we  can  discover  a  connect- 
ing thread  or  common  element  between  two  facts  or 
groups  of  facts,  we  are  able  to  infer  with  greater  or  less 
certainty  from  the  nature  of  the  one  what  the  nature  of 
the  other  must  be.  But  it  is  essential  to  inference  that 
there  shall  be  a  real  transition  from  one  fact  to  another  — 
that  the  conclusion  reached  shall  be  different  from  the 
starting-point. 

The  point  at  issue,  therefore,  is  whether  a  new  fact  or  truth 
is  reached  in  the  so-called  processes  of  immediate  inferences, 
or  whether  we  have  the  same  fact  repeated  in  the  form  of  a  new 
proposition.  When  we  pass  from  '  no  men  are  infallible,'  to 
'no  infallible  beings  are  men,'  can  we  be  said  to  infer  a  new 
truth?  In  this  case  it  is  evident,  I  think,  that  there  has  been  nc 
real  development  or  extension  of  the  original  proposition  so  as 
to  include  a  new  fact.  The  new  proposition  is  the  result  of  a 
verbal  interpretation  of  the  original  one,  and  restates  the  same 
fact  in  a  different  way.  Inference  always  completes  or  enlarges 
the  truth  from  which  it  sets  out  by  showing  the  reasons  which 
support  it,  or  the  consequences  which  follow  from  it.  Now, 
when  we  pass  directly  from  one  proposition  to  another,  as 


§  25.    The  Opposition  of  Propositions  99 

in  the  examples  given  above,  it  will  be  found,  I  believe, 
that  nothing  new  has  been  added  to  the  original  state- 
ment —  no  new  facts  have  been  brought  into  connection 
in  the  process. 

Nevertheless,  the  process  does  not  appear  to  be  merely 
verbal,  but  to  involve  a  certain  movement  of  mind,  —  a  fuller 
and  clearer  realization  of  the  meaning  and  bearings  of  the 
original  proposition.  Before  deciding  the  matter,  the  claims 
of  each  of  the  different  types  of  so-called  immediate  inference 
should  be  examined  separately;  and  the  question  is  one  that 
the  student  should  keep  in  mind  throughout  the  chapter. 
Some  authors  have  named  these  processes  '  Eduction,'  since 
they  draw  out  or  explicate  the  meaning  of  propositions. 
Whether  or  not  they  may  properly  be  called  inference,  they 
render  important  service  in  helping  us  to  understand  all 
that  is  really  implied,  both  in  the  way  of  affirmation  and 
denial,  in  the  propositions  we  use.  Nothing  is  commoner  in 
argument  than  disputes  as  to  what  certain  statements  imply  — 
what  propositions  '  amount  to  the  same  thing,'  and  may  there- 
fore properly  be  substituted  for  any  given  statement.  Now  it 
is  the  purpose  of  the  methods  of  logical  interpretation  (or  im- 
mediate inference)  which  are  to  be  discussed  in  this  chapter,  to 
determine  what  other  statements,  positive  or  negative,  are 
really  involved  in  the  case  of  the  different  forms  of  logical  propo- 
sition. Given  a  certain  proposition  as  true  or  false,  what  other 
propositions  can  be  immediately  derived  from  it  ?  We  may 
consider  under  the  following  five  headings  the  results  obtain- 
able by  processes  of  Immediate  Inference,  or  direct  Interpreta- 
tion: Opposition,  Obversion,  Conversion,  Contraposition, 
Inversion. 

§  25.   The  Opposition  of  Propositions. —  We  have  seen  that 


ioo  The  Interpretation  of  Propositions 

all  categorical  propositions  have  to  be  reduced  to  one  of  tnt 
four  forms,  A,  E,  I,  O,  in  order  to  be  dealt  with  by  logic.  Now, 
between  these  propositions,  all  of  which  have  the  same  subject 
and  predicate,  certain  relations  of  exclusion  and  inclusion  exist, 
to  which  the  general  name  of  Opposition  has  been  given.  It  is 
clear  that  the  truth  of  some  of  these  propositions  excludes  the 
truth  cf  others,  and  also  that  the  relation  between  certain  of 
the  propositions  is  such  that  one  assertion  necessarily  involves 
the  truth  of  another.  Logical  Opposition,  then,  is  used  to 
denote  any  relation,  either  of  exclusion  or  inclusion,  that  exists 
between  propositions  having  the  same  subject  and  predicate. 
Thus,  if  it  be  true  that  '  no  professional  gamblers  are  honest,' 
it  is  impossible  that  '  all  professional  gamblers  are  honest,'  or 
even  that  some  are  honest.  The  proposition  E  is  thus  incon- 
sistent with  both  A  and  I.  Again,  if  it  be  true  that '  all  politi- 
cians are  dishonest,'  it  must  be  true  that  '  some  politicians  are 
dishonest,'  as  well  as  false  that  'no  politicians  are  dishonest.' 
That  is,  when  A  is  true,  I  is  also  true,  while  E  is  necessarily 
false.  Propositions  A  and  E  are  called  Contrary  propositions. 
'  All  A  is  B,'  and  '  no  A  is  B,'  express  the  greatest  possible  de- 
gree of  contrariety  or  opposition.  If  one  proposition  be  true, 
the  other  is  necessarily  false.  It  is  to  be  noticed,  however, 
that  we  cannot  conclude  that  if  one  be  false,  the  other  is  true. 
For  both  A  and  E  may  be  false.  Thus,  for  example,  the 
propositions, '  all  men  are  wise  '  and  '  no  men  are  wise,'  are 
both  false.  But,  on  the  other  hand,  propositions  A  and  O, 
E  and  I,  are  pairs  of  Contradictory  propositions:  if  one  is  false, 
its  contradictory  is  necessarily  true;  and  if  one  is  true,  the 
other  is  manifestly  false. 

The  relation   of  the  four  logical   propositions  is  clearly 
shown  by  arranging  them  in  the  following  way:  — 


§  25.    The  Opposition  of  Propositions 


IOI 


Contraries 


x  c> 

X  o~ 

V"* 

\V                   / 

X°/                                  X 

to 

u> 

c 

E 

0) 

o 

M 

.«?/           X 

o 

3 

3 
CO 

CO 

j  Sub-Contraries  O 

Fig.  5. 

A  and  E  are  known  as  contraries;  I  and  O  as  subcontraries; 
A  and  O,  I  and  E,  as  contradictories;  A  and  I,  E  and  O,  as 
subalterns. 

The  relations  of  these  propositions  may  now  be  summed  up 
in  the  following  statements:  — 

(1)  Of  contrary  propositions,  one  is  false  if  the  other  is  true, 
but  both  may  be  false. 

(2)  Of  contradictory  propositions,  one  is  true  and  the 
other  necessarily  false. 

(3)  If  a  universal  proposition  is  true,  the  particular  which 
stands  under  it  is  also  true;  but  if  the  universal  ?s  false,  the 
particular  may  or  may  not  be  true. 

(4)  If  a  particular  proposition  is  true,  the  corresponding 
universal  may  or  may  not  be  true;  but  if  the  particular  is  false, 
the  universal  must  be  false. 


102  The  Interpretation  of  Propositions 

(5)  Subcontrary  propositions  may  both  be  true  ;  but  if  one 
is  false,  the  other  is  necessarily  true. 

The  knowledge  that  any  one  of  these  propositions  is  either 
true  or  false  enables  us  to  determine  the  truth  or  falsity  of  at 
least  some  of  the  others. 

For  example,  if  A  is  true,  E  is  false,  O  is  false,  and  I  is  true. 
If  A  is  false,  E  is  doubtful,  O  is  true,  and  I  doubtful. 

If  I  is  true,  E  is  false,  A  is  doubtful,  and  O  doubtful.  If  I  is 
false,  E  is  true,  A  is  false,  and  O  true. 

Similarly,  we  are  also  able  to  determine  what  follows  when 
we  suppose  that  E  and  O  are  either  false  or  true. 

It  ought  to  be  carefully  noted  that  when  we  affirm  the  truth  of 
the  particular  proposition  I,  we  do  not  deny  the  truth  of  the  universal 
proposition  A.  The  proposition, '  some  students  are  fond  of  recrea- 
tion,' for  example,  does  not  exclude  the  truth  of  '  all  students  are 
fond  of  recreation.'  Similarly,  the  truth  of  O  does  not  exclude  the 
corresponding  proposition  in  E:  the  statement,  'some  men  are  not 
generous,'  for  example,  does  not  interfere  with  the  truth  of  the  uni- 
versal proposition, '  no  men  are  generous. '  A  particular  proposition, 
in  other  words,  asserts  something  of  a  limited  part  of  a  subject; 
it  neither  affirms  nor  denies  anything  of  the  same  term  taken 
universally. 

The  reader  will  remember  that  propositions  which  have 
the  name  of  some  singular  or  individual  thing  as  subject,  have 
been  classified  as  universal.  '  New  York  is  the  largest  city  in 
America,'  'charity  is  not  the  only  virtue,'  are  examples  of  such 
propositions.  Now  it  is  at  once  evident  that  in  cases  of  this 
kind  there  are  no  corresponding  particular  propositions. 
What  has  just  been  said  regarding  the  relation  of  universal 
and  particular  propositions,  applies  therefore  only  to  propo- 
sitions which    have    a  general  term    or  name   as  subject. 


§  26.    The  Obversion  of  Propositions  103 

Moreover,  we  must  notice  that  when  A  and  E  proposi- 
tions have  a  singular  or  individual  name  as  subject,  the 
relations  between  them  are  somewhat  different  from  those 
just  stated.  A  and  E,  we  said,  are  contrary,  but  not  contradic- 
tory propositions.  By  that  it  was  implied  that  although  we 
can  proceed  from  the  truth  of  the  one  to  the  falsity  of  the  other, 
it  is  not  possible  to  go  in  a  converse  direction,  from  falsity  to 
truth.  We  cannot  conclude,  for  example,  from  the  falsity  of 
the  proposition  that '  all  men  are  selfish '  the  truth  of  the  corre- 
sponding negative  proposition,  'no  men  are  selfish.'  With 
contradictory  propositions,  however,  we  can  go  from  a 
denial  to  an  affirmation.  Now  the  point  to  be  observed,  with 
regard  to  propositions  with  a  singular  term  as  subject,  is  that 
although  only  contraries  in  form,  they  have  yet  the  force  of 
contradictories.  'Socrates  is  wise'  (A),  and  'Socrates  is  not 
wise'  (E),  are  contradictory,  as  well  as  contrary,  propositions. 

§  26.  The  Obversion  of  Propositions.  —  The  terms  '  Ob- 
version  '  and  '  ^quipollence '  were  formerly  used  to  denote 
any  process  by  which  the  form  of  a  proposition  is  changed 
without  an  alteration  in  meaning  being  involved.  The 
name  'Obversion'  is,  however,  now  generally  employed  to 
describe  the  change  which  a  proposition  undergoes  in  passing 
from  the  affirmative  to  the  negative,  or  from  the  negative  to 
the  affirmative  form  while  still  retaining  its  original  meaning. 

Every  fact  is  capable  of  expression  either  in  the  form 
of  an  affirmative  or  of  a  negative  proposition.  Whether 
the  affirmative  or  negative  form  is  chosen  in  any  particular 
case,  is  partly  a  matter  of  convenience.  It  is  also  deter- 
mined largely  by  the  psychological  interest  of  the  moment, 
i.e.  by  the  purpose  which  we  have  in  view  in  making  the 
assertion.     When,  for  example,  we  wish  to  repel  some  sug- 


104  The  Interpretation  of  Propositions 

gestion  which  may  have  occurred  to  us,  or  to  deny  something 
which  our  companions  appear  to  believe,  we  naturally  choose 
the  negative  form  of  statement.  But  the  meaning  of  the 
proposition  is  the  same  whether  we  say,  '  all  men  are  falli 
ble,'  or,  'no  men  are  infallible.'  Similarly,  we  can  say,  'not 
one  of  the  crew  escaped,'  or,  '  all  of  the  crew  perished.' 

Obversion,  then,  is  the  process  of  substituting  for  any 
affirmative  proposition  its  equivalent  in  negative  form, 
or  of  expressing  the  meaning  of  a  negative  proposition  as  an 
affirmative.  To  obtain  the  obverse  of  proposition  A,  we 
proceed  on  the  principle  that  two  negatives  are  equal  to  an 
affirmative.  Instead  of  '  all  animals  digest  food,'  we  may 
write,  '  no  animals  are  beings  that  do  not  digest  food';  for, 
'  every  man  has  his  own  troubles,'  '  there  are  no  men  who 
have  not  their  own  troubles.'  Instead  of  affirming  the 
predicate  of  the  subject,  the  obverse  of  A  takes  the  contra- 
dictory of  the  original  predicate  and  denies  it  universally. 

Proposition  I  may  be  obverted  in  the  same  way,  though 
it  yields  a  particular,  instead  of  a  universal  negative  propo- 
sition. Thus  the  obverse  of,  '  some  of  the  houses  are  com- 
fortable,' is  '  some  of  the  houses  are  not  not-comfortable,' 
i.e.  uncomfortable.  We  deny  the  negative  predicate  in  the 
obverse  proposition,  instead  of  affirming  the  positive. 

We  obtain  the  obverse  of  the  propositions  E  and  O  by 
changing  the  negation  contained  in  them  to  its  equivalent 
affirmation.  This  is  done  by  attaching  the  negative  to  the 
predicate,  and  then  affirming  it  of  the  subject.  For  example, 
to  obtain  the  obverse  of,  '  no  one  who  was  present  can  forget 
the  scene,'  we  first  write  the  proposition  in  logical  form, 
'  no  one  who  was  present  is  a  person  who  can  forget  the  scene.' 
Now  the  contradictory  of  the  predicate  term,  '  a  person  who 


§  2y.    The  Conversion  of  Propositions  105 

can  forget  the  scene,'  is,  '  a  person  who  can  not  forget  the 
scene.'  Affirming  this  universally  we  get,  '  all  persons  who 
were  present  are  persons  who  cannot  forget  the  scene.'  As 
an  example  of  how  the  obverse  of  O  is  obtained,  we  may 
take  the  proposition,  '  some  metals  are  not  white.'  Now  if 
we  change  the  quality  of  the  proposition  by  attaching  the 
negative  to  the  predicate,  we  obtain,  '  some  metals  are  not- 
white.'  That  is,  instead  of  denying,  we  affirm  the  contra- 
dictory of  the  original  predicate.  When  the  predicate  is  made 
up  of  several  words,  it  is  important  that  the  logical  contra- 
dictory of  the  whole  term  be  taken.  For  example,  in  the 
proposition,  '  some  men  are  not  fond  of  work,'  the  predicate 
fully  expressed  is,  '  persons  who  are  fond  of  work.'  Now 
the  negative  or  contradictory  term  corresponding  to  this  is, 
'  persons  who  are  not  fond  of  work.'  The  obverse  of  the 
original  proposition  therefore  is,  '  some  men  are  persons 
who  are  not  fond  of  work.' 

§  27.  The  Conversion  of  Propositions.  — To  convert  a 
proposition  is  to  transpose  its  subject  and  predicate  so  that 
each  shall  occupy  the  place  previously  held  by  the  other. 
Thus  the  proposition,  '  no  men  are  infallible,'  is  converted 
by  writing  it,  '  no  infallible  beings  are  men.'  The  original 
proposition  is  called  the  Convertend,  and  the  proposition 
obtained  by  conversion  the  Converse.  By  conversion,  then, 
a  proposition  having  P  as  its  subject  is  derived  directly 
from  the  original  form  of  the  assertion  S  — P.  It  is  for  this 
reason  that  conversion  is  usually  ranked  as  a  process  of 
immediate  inference.  For  it  makes  clear  what  is  involved 
in  the  original  proposition  but  is  perhaps  not  clearly  rec- 
ognized ;  namely,  that  in  the  assertion  S  —  P  some  statement 
about   P   as  subject   in  its  relation  to  S  is  also   involved 


IO0  The  Interpretation  of  Propositions 

Whether  this  may  more  properly  be  regarded  as  a  process  of 
formal  interpretation,  than  as  one  which  involves  real  infer- 
ence, is  a  question  which  the  student  may  consider  for  himself. 

It  is  evident  that  in  proceeding  to  convert  propositions 
it  will  be  necessary  to  notice  whether  the  predicate  of  the 
convertend,  or  proposition  to  be  converted,  is  distributed 
or  undistributed,  otherwise  we  should  not  know  what  exten- 
sion to  apply  to  this  term  when  used  as  the  subject  of  the 
converse  proposition.  The  rules  usually  given  to  limit 
the  process  of  conversion  are  as  follows:  — 

(i)  No  term  must  be  distributed  in  the  converse  propo- 
sition which  was  not  distributed  in  the  convertend. 

(2)  The  quality  of  the  converse  proposition  must  remain 
the  same  as  the  quality  of  the  convertend. 

The  reason  for  the  first  rule  is  at  once  evident  from  what 
has  been  already  said.  The  second  rule  is  not  one  which  is 
always  observed.  Of  course,  the  meaning  of  a  proposition 
must  not  be  altered  by  changing  the  quality  simply  or 
directly.  But,  in  converting  by  Contraposition,  as  we  shall 
see  later,  it  is  first  necessary  to  obtain  the  equivalent  of 
the  convertend  by  ob version,  and  this  necessarily  involves 
a  change  of  quality. 

There  are  two  kinds  of  conversion  usually  recognized: 
(a)  Simple  Conversion;  (b)  Conversion  by  Limitation  or 
per  accidens. 

(a)  By  Simple  Conversion  is  meant  the  direct  transposition 
of  the  subject  and  predicate  without  any  other  change  in 
the  form  of  the  proposition.  Both  propositions  E  and  I 
can  be  converted  in  this  way.  Thus  the  converse  of, '  none  of 
the  books  on  this  shelf  are  novels,'  is  another  proposition  in 
E,  '  no  novels  are  books  on  this  shelf.'     From  '  some  dicoty- 


§  27.    The  Conversions  of  Propositions  107 

ledons  are  exogens  '  we  obtain  by  conversion  another  particu- 
lar affirmative  proposition, '  some  exogens  are  dicotyledons.' 

(b)  Conversion  by  Limitation  or  per  accidens  is  applied 
to  proposition  A.  In  this  process  A  loses  its  universality, 
and  yields  as  a  result  only  proposition  I.  To  illustrate 
this  mode  of  conversion  we  may  take  the  proposition, '  brown 
hematite  is  an  iron  ore.'  As  we  already  know,  the  term 
'an  iron  ore,'  being  the  predicate  of  proposition  A,  is  undis- 
tributed. When  used  as  the  subject  of  a  new  proposition, 
therefore,  it  must  be  limited  by  the  adjective  '  some.'  We 
thus  obtain  the  converse  proposition,  '  some  iron  ore  is 
brown  hematite.'  Similarly,  the  converse  of  the  proposition, 
'  all  sensations  are  mental  processes,'  is  '  some  mental  pro- 
cesses are  sensations.'  When  proposition  A  is  converted  by 
limitation,  then,  it  yields  proposition  I  as  a  result.  And  it 
is  evident  that  the  proposition  has  really  lost  something  in 
the  process.  For  it  is  impossible  by  converting  again  to 
obtain  anything  more  than  a  particular  proposition.  It  is, 
however,  sometimes  possible  to  convert  proposition  A  with- 
out limiting  the  predicate.  In  formal  definitions,  for  example, 
the  subject  and  the  predicate  are  of  equal  extent,  and  may  be 
transposed  simply  without  any  limitation  of  the  latter.  Thus 
the  converse  of,  '  an  equilateral  triangle  is  a  plane  figure 
having  three  equal  sides,'  is  '  a  plane  figure  having  three 
equal  sides  is  an  equilateral  triangle.' 

Proposition  O  is  the  only  form  of  logical  proposition  that 
does  not  admit  of  Conversion.  E  and  I,  as  we  have  seen, 
may  be  converted  simply,  and  the  converse  of  A  is  obtainable 
by  limitation,  or  even  in  some  cases  by  simple  Conversion. 
But  from  an  O  proposition,  '  some  S  is  not  P,'  no  proposition 
where  P  is  subject  and  S  predicate  can  be  obtained.     And 


io8  The  Interpretation  of  Propositions 

ttie  reason  for  this  may  be  seen  at  once.  For  if  the  conver 
sion  were  made,  giving  the  form  'some  P  is  not  S,'  S  would 
be  distributed  as  the  predicate  of  a  negative  proposition. 
But  in  the  convertend  ('  some  S  is  not  P  ')  it  was  not  distrib- 
uted; accordingly,  an  attempt  to  convert  O  involves  a  breach 
of  the  rule  that  no  term  must  be  distributed  in  the  converse 
proposition  which  was  not  distributed  in  the  convertend. 

§  28.  Contraposition  and  Inversion.  —  In  Contraposition 
the  contradictory  of  the  predicate  of  the  original  proposition 
is  taken  as  the  subject  of  a  new  assertion.  That  is,  the  Contra- 
positive  of  a  proposition  of  the  form  S  —  P,  has  as  its  subject 
non-P,  the  contradictory  of  P.  Contrapositive  propositions 
may  be  derived  from  A,  E,  and  O.  Proposition  I,  for  reasons 
that  will  be  evident  later,  does  not  yield  a  contrapositive. 

The  contrapositive  of  A,  E,  and  O  may  be  obtained 
through  two  steps:  by  first  ob verting  and  then  converting. 
After  some  practice  in  deriving  the  contrapositive  in  this 
way  the  student  should  learn  to  obtain  it  directly,  remem- 
bering that  what  is  required  is  a  statement  as  to  what  is 
implied  in  the  original  proposition  regarding  non-P,  the 
contradictory  of  the  predicate.  Let  us  first,  however,  illus- 
trate the  longer  method. 

If  we  take  as  an  example  of  A  the  proposition  '  all  the  plan- 
ets are  bodies  that  revolve  around  the  sun,'  we  can  obtain 
the  contrapositive  by  (1)  obverting, 'no  planets  are  bodies 
that  do  not  revolve  around  the  sun,'  and  (2)  converting  the 
E  proposition  obtained  by  ob  version,  'No  bodies  that  do  not 
revolve  around  the  sun  are  planets.'  This  is  in  the  form 
'  no  non-P  is  S,'  and  we  might  therefore  write  the  contra- 
positive of  A  directly,  by  taking  the  contradictory  of  the 
original  predicate  and  denying  it  universally  of  the  subject. 


§  28.    Contraposition  and  Inversion  109 

The  form  here  derived,  the  converse  of  the  obverse,  has 
usually  been  denned  as  the  contrapositive  of  a  given  propo- 
sition, and  we  have  so  far  followed  this  definition.  But 
some  logicians  speak  of  the  contrapositive  as  a  proposition 
which  has  the  same  quality  as  the  original,  and  has  the  more 
symmetrical  form  '  non-P  — non-S.'  This  maybe  obtained 
by  ob verting  the  result  obtained  in  the  last  paragraph, 
'all  bodies  that  do  not  revolve  around  the  sun  are  non- 
planets.'  The  two  forms  are  not  essentially  different,  but 
we  may  follow  what  appears  to  be  the  best  usage  by  speaking 
of  the  form  '  non-P  —  S,'  as  the  partial  contrapositive,  and 
'non-P — non-S'  as  the  full  contrapositive. 

Taking  as  an  example  of  E  the  proposition  '  none  that 
love  angling  are  wholly  given  over  to  the  world,'  we  obtain 
(1)  by  Ob  version, '  all  that  love  angling  are  persons  not  wholly 
given  over  to  the  world,'  and  (2)  by  Conversion  of  this  latter 
proposition,  '  some  persons  not  wholly  given  over  to  the 
world  are  those  who  love  angling.'  This  is  the  partial 
contrapositive,  which  when  obverted  gives  us  the  full  contra- 
positive, '  some  persons  not  wholly  given  over  to  the  world 
are  not  those  who  do  not  love  angling,'  a  negative  proposition 
like  the  E  from  which  it  is  derived,  and  which  has  the  form 
'  some  not-P  is  not  not-S.'  It  is  especially  to  be  noted 
that  the  contrapositive  of  E  is  a  particular  proposition. 

To  obtain  the  contrapositive  of  O,  we  proceed  in  the  same 
way,  first  ob  verting,  then  converting  the  result  for  the 
partial  contrapositive,  and  ob  verting  once  more  for  the 
full  contrapositive.  For  example,  'some  things  that  glitter 
are  not  gold';  (1)  by  obversion,  'some  things  that  glitter 
are  not-gold '  (i.e.  substances  other  than  gold) ;  (2)  by  con- 
version, '  some  substances  other  than  gold  are  things  that 


HO  The  Interpretation  of  Propositions 

glitter';    (3)  by  ob version,  'some  substances  other  than  gold 
are  not  things  that  do  not  glitter.' 

Inversion.  The  original  proposition  has  S  as  subject  and 
P  as  predicate;  the  converse  has  P  as  subject  and  S  as 
predicate  ;  the  contrapositive,  non-P  as  subject,  and  in  its 
full  form,  non-S  as  predicate.  It  is  clear  that  the  only  remain- 
ing term  to  be  used  as  a  subject  is  non-S.  Now,  where  an 
assertion  is  made  regarding  this  —  the  contradictory  of  the 
original  subject  —  the  form  is  known  as  the  Inverse.  The 
question  now  is:  What  logical  propositions  of  the  form 
S  —  P  enable  us  to  derive  a  proposition  about  what  is  not-S  ? 
By  experimenting  in  applying  obversion  and  conversion  we 
find  that  only  the  Universal  propositions,  A  and  E,  yield 
the  Inverse  form,  and  also  that  this  is  always  a  particular 
proposition.  From  'All  S  is  P,'  we  may  derive,  by  alternately 
ob  verting  and  converting,  'some  not-S  is  not-P'  (which  may 
be  called  the  full  Inverse  by  analogy  with  the  terms  em- 
ployed in  regard  to  contraposition),  which  by  obversion 
gives  '  some  not-S  is  not  P,'  the  partial  Inverse.1  Similarly, 
beginning  with  conversion,  and  then  obverting  and  convert- 
ing, from  '  no  S  is  P '  may  be  derived  the  partial  Inverse, 

1  Keynes  {Formal  Logic,  4th  ed.,  pp.  139-40)  calls  attention  to  the  apparent 
error  in  passing  from 'All  S  isP,' — where  P  is  not  distributed  —  to,  'Some  not 
S  is  not  P,'  —  where  P  is  distributed.  The  result  seems  an  error,  yet  it  is 
impossible  to  discover  any  mistake  in  the  processes  of  conversion  and  obversion 
by  which  it  has  been  obtained.  This  difficulty  may  serve  to  illustrate  the 
impossibility  of  proceeding  logically  without  assumptions  even  where  the  trans- 
formations appear  to  be  purely  formal.  Keynes  says:  "It  is  in  the  assumption 
of  the  existence  of  the  contradictory  of  the  original  predicate  that  an  explanation 
of  the  apparent  anomaly  may  be  found.  That  assumption  may  be  expressed 
in  the  form,  'Some  things  are  not  P.'  The  conclusion  'Some  not-S  is  not  P' 
may  accordingly  be  regarded  as  based  on  this  premise  combined  with  the  ex- 
plicit premise,  'All  S  is  P';  and  it  will  be  observed  that,  in  the  additional 
premise,  P  is  distributed." 


§  28.     Contraposition  and  Inversion 


ill 


'  some  not-S  is  P,'  which  yields,  by  obversion,  the  full  In- 
verse, '  some  not-S  is  not  not-P.' 

We  have  already  summarized  results  with  regard  to  the 
Opposition  of  propositions  (p.  101).  For  the  sake  of  con- 
venience the  outcome  of  the  other  processes  may  be  brought 
together  in  the  following  table,  given  by  Keynes.1  S'  and  P' 
are  used  to  denote  not-S  and  not-P. 


A 

I 

E 

O 

Original  proposition 

.  SaP 

SiP 

SeP 

SoP 

ii 

Obverse 

SeP' 

SoP' 

SaP' 

SiP' 

iii 

Converse 

PiS 

PiS 

PeS 

iv 

Obverted  Converse 

PoS' 

PoS' 

PaS' 

V 

Partial  Contrapositive 

P'eS 

P'iS 

P'iS 

vi 

Full  Contrapositive 

P'aS' 

P'oS' 

P'oS' 

vii 

Partial  Inverse 

S'oP 

S'iP 

viii 

Full  Inverse 

S'iP' 

S'oP' 

REFERENCES 


B.  Bosanquet,  Logic,  Vol.  I.,  pp.  310-319. 
W.  Minto,  Logic  Inductive  and  Deductive,  Pt.  III.,  pp.  130--166. 
J.  N.  Keynes,  Studies  and  Exercises  in  Formal  Logic,  4th  ed.,  Chs. 
III.,  and  IV. 

1  Op.  cit.,  p.  14a 


CHAPTER  VIII 

THE     SYLLOGISM 

§  29.  The  Nature  of  Syllogistic  Reasoning.  —  The  syl- 
logism, as  we  have  already  seen  (§  10),  presents  a  conclusion 
together  with  the  reasons  by  means  of  which  it  is  supported. 
A  single  proposition  taken  by  itself  is  dogmatic:  it  merely 
asserts,  without  stating  the  grounds  upon  which  it  rests. 
The  syllogism,  on  the  other  hand,  justifies  its  conclusion 
by  showing  the  premises  from  which  it  has  been  derived. 
It  thus  appeals  to  the  reason  of  all  men,  and  compels  their 
assent.  To  do  this,  it  is  of  course  necessary  that  the  truth  of 
the  premises  to  which  appeal  is  made  should  be  granted. 
If  the  premises  are  disputed  or  doubtful,  the  argument 
is  pushed  a  step  further  back,  and  it  is  first  necessary  to 
show  the  grounds  upon  which  these  premises  rest.  The 
assumption  of  syllogistic  reasoning  —  and,  indeed,  of  all 
reasoning  whatsoever  —  is  that  it  is  possible  to  reach 
propositions  which  every  one  will  accept.  There  are  certain 
facts,  we  say,  well  known  and  established,  and  these  can 
always  be  appealed  to  in  support  of  our  conclusions.  In 
syllogistic  reasoning,  then,  we  exhibit  the  interdependence  of 
propositions;  i.e.,  we  show  how  the  truth  of  some  new  propo- 
sition, or  some  proposition  not  regarded  as  beyond  question, 
follows  necessarily  from  other  propositions  whose  truth 
every  one  will  admit. 


§  29.    The  Nature  of  Syllogistic  Reasoning        113 

The  question  which  arises  in  connection  with  the  syllogism, 
therefore,  is  this:  Under  what  conditions  do  propositions  which 
are  accepted  as  true  contain  or  imply  a  new  proposition  as  a 
conclusion?  Or  we  may  put  the  question  in  this  form:  In 
what  ways  may  the  four  kinds  of  logical  propositions,  A,  E,  I, 
O,  be  combined  so  as  to  yield  valid  conclusions  ? 

We  pointed  out  in  a  previous  chapter  that  a  syllogism  has 

always  two  premises.     It  is,  however,  impossible  to  obtain  a 

conclusion  by  combining  any  two  propositions  at  random, 

as  e.g.— 

All  A  is  B, 

No  X  is  Y. 

It  is  evident  that  any  two  propositions  will  not  yield  a  con- 
clusion by  being  taken  together.  In  order  to  serve  as  premises 
for  a  syllogism,  propositions  must  fulfil  certain  conditions,  and 
stand  in  certain  definite  relations  to  each  other.  To  deter- 
mine some  of  the  most  apparent  of  these  conditions,  let  us 
examine  the  argument :  — 

All  mammals  are  vertebrates, 
The  whale  is  a  mammal, 
Therefore  the  whale  is  a  vertebrate. 

It  will  be  noticed  that  the  term  '  mammal '  is  common  to  both 
premises,  and  that  it  does  not  occur  at  all  in  the  conclusion. 
Moreover,  it  is  because  the  other  terms  are  compared  in  turn  with 
this  common  or  Middle  Term  and  found  to  agree  with  it,  that 
they  can  be  united  in  the  conclusion.  It  is  only  propositions 
which  have  a  middle  term,  therefore,  which  can  be  employed 
as  the  premises  of  a  syllogism.  The  syllogism  is  thus  essen- 
tially a  process  of  comparison.  Each  of  the  terms  entering  into 
the  conclusion  is  compared  in  turn  with  the  same  middle  term, 


1 14  The  Syllogism 

and  in  this  way  their  relation  to  each  other  is  determined. 
We  reach  the  conclusion  not  directly  or  immediately,  but 
by  means  of  the  middle  term.  The  conclusion  is  therefore 
said  to  be  mediated,  and  the  process  itself  is  sometimes  called 
mediate  reasoning. 

It  will  be  interesting  to  compare  what  has  just  been  said  regard- 
ing the  function  of  the  middle  term,  with  what  has  been  previously 
stated  regarding  the  nature  of  inference.  When  we  infer  one  fact 
from  another,  it  was  said,  we  do  so  by  discovering  some  identical  link 
or  connecting  thread  which  unites  both.  We  may  say  that  to  infer 
is  to  see  that,  in  virtue  of  some  identical  link  which  our  thought  has 
brought  to  light,  the  two  facts,  or  groups  of  facts,  are  in  a  certain 
sense  identical.  Now  the  middle  term  in  a  syllogism  is  just  the 
explicit  statement  of  the  nature  of  this  identical  link.  It  is  true  that 
in  the  syllogism  we  seem  to  be  operating  with  words  or  terms  rather 
than  with  the  thought-process  itself.  When  we  go  behind  the 
external  connection  of  the  terms,  however,  we  can  see  that  the 
middle  term  represents  the  universal  principle,  by  means  of  which 
the  conclusion  is  reached.  In  the  example  given  above,  for  in- 
stance, we  reason  that  the  whale,  being  a  mammal,  is  a  vertebrate. 

The  terms  which  enter  into  the  conclusion  of  a  syllogism 
are  sometimes  called  the  Extremes,  as  opposed  to  the  middle 
term.  Of  the  Extremes,  the  predicate  of  the  conclusion  is 
known  as  the  Major  Term,  and  the  subject  of  the  conclusion  as 
the  Minor  Term.  The  premise  which  contains  the  major 
term  is  called  the  Major  Premise,  and  stands  first  when 
the  syllogism  is  arranged  in  logical  form.  The  Minor  Premise 
on  the  other  hand,  is  the  premise  which  contains  the  minor 
term,  and  it  stands  second  in  the  arrangement  of  the  syllogism. 
The  propositions  of  which  the  syllogism  is  composed  may  occur, 
however,  in  any  order  in  actual  reasoning;  either  premise,  or 


§  30-    The  Rules  of  the  Syllogism  115 

even  the  conclusion,  may  stand  first.  To  arrange  an  argu- 
ment, therefore,  it  is  necessary  to  determine  which  is  the  major, 
and  which  is  the  minor  premise.  This  can  be  done  most 
readily  by  turning  to  the  conclusion,  and  distinguishing  the 
major  and  minor  terms.     For  example,  take  the  syllogism:  — 

The  whale  suckles  its  young, 
No  fish  suckles  its  young, 
Therefore  the  whale  is  not  a  fish. 

By  turning  to  the  conclusion  we  see  that  '  fish '  (being  the 
broader  term  and  therefore  naturally  predicate)  is  the  major 
term.  The  proposition  which  contains  this  term,  '  no  fish 
suckles  its  young, '  is,  therefore,  the  major  premise,  and  should 
stand  first.  Before  proceeding  to  examine  the  syllogism 
further  it  would  be  necessary  to  arrange  it  as  follows :  — 

No  fish  is  an  animal  which  suckles  its  young, 
The  whale  is  an  animal  which  suckles  its  young, 
Therefore  the  whale  is  not  a  fish. 

§  30.  The  Rules  of  the  Syllogism.  — It  is  customary  to  give 
a  number  of  rules  or  canons  to  which  the  syllogism  must  con- 
form in  order  b  yield  valid  conclusions.  We  shall  first  enu- 
merate the  rules,  and  afterwards  remark  on  their  meaning 
and  importance. 

(1)  In  every  syllogism  there  should  be  three,  and  only  three, 
terms,  and  these  terms  must  be  used  throughout  in  the  same 
sense. 

The  terms,  as  we  have  already  remarked,  are  known  as  the 
major  term,  the  middle  term,  and  the  minor  term. 

(2)  Every  syllogism  contains  three,  and  only  three, 
propositions. 


Ii6  The  Syllogism 

These  are  called  the  major  premise,  minor  premise,  and 
conclusion. 

(3)  The  middle  term  must  be  distributed  in  at  least  one  of 
the  premises. 

(4)  No  term  must  be  distributed  in  the  conclusion  which 
was  not  distributed  in  one  of  the  premises. 

(5)  From  negati  ve  premises  nothing  can  be  inferred. 

(6)  If  one  premise  be  negati  ve,  the  conclusion  must  be  nega- 
tive;  and,  conversely,  to  prove  a  negative  conclusion  one  of 
the  premises  must  be  negative. 

As  a  consequence  of  the  above  rules  there  result  two  addi- 
tional canons  which  may  be  set  down  here. 

(7)  No  conclusion  can  be  drawn  from  two  particular 
premises. 

(8)  If  one  of  the  premises  be  particular,  the  conclusion 
must  be  particular. 

The  reason  for  the  first  and  second  rules  will  be  evident 
from  what  has  been  already  said  about  the  structure  of  the 
syllogism.  We  saw  that  a  logical  argument  is  a  process  of 
comparison;  that  two  terms  are  united  through  comparing 
them  with  a  common  or  middle  term.  If  the  meaning  of  the 
terms  does  not  remain  fixed,  there  are  more  than  three  terms, 
and  no  comparison  is  possible.  The  second  rule  follows  as 
a  corollary  from  the  first. 

The  third  rule,  that  the  middle  term  must  be  distributed 
once,  at  least,  is  extremely  important,  and  its  necessity  will  be 
readily  perceived.  For,  since  the  middle  term  is  the  standard 
of  comparison,  it  must  be  used  in  at  least  one  premise  in  its 
universal  extent.  Otherwise  we  might  compare  the  major 
term  with  one  part  of  it,  and  the  minor  term  with  another  part. 
Such  a  comparison  would  of  course  not  warrant  us  in  either 


§  3°-    The  Rules  of  the  Syllogism  117 

affirming  or  denying  the  connection  of  these  terms  in  the  con- 
clusion.    For  example,  the  two  propositions,  — 
Sedimentary  rocks  are  stratified  substances, 
Some  metamorphic  rocks  are  stratified  substances, 
do  not  distribute  the  middle  term,  '  stratified  substances, '  at 
all,  being  both  affirmative  propositions.      It  is  clear  that  the 


Fig.  6. 
term,  c  sedimentary  rocks, '  agrees  with  one  part  of  the  strati- 
fied substances,  and  '  metamorphic  rocks '  with  another  part. 
We  are,  therefore,  not  able  to  infer  that  '  some  metamorphic 
rocks  are  sedimentary  rocks.'  This  may  be  clearly  shown  by 
representing  the  propositions  by  Euler's  method  of  circles  as 
in  Fig.  6.  We  know  from  the  second  proposition  that  the  circle 
representing  '  metamorphic  rocks '  falls  partly  within  the 
circle  of '  stratified  substances.'  But  it  is  impossible  to  deter- 
mine from  the  statement  whether  it  corresponds  at  all  with 
the  circle  of  sedimentary  rocks,  or  falls,  as  in  the  figure, 
entirely  without  it. 

The  fourth  rule  states  that  no  term  must  be  distributed  in  the 
conclusion  which  was  not  distributed  in  one  of  the  premises. 
That  is,  the  conclusion  must  be  proved  by  means  of  the  prem- 
ises, and  no  term  which  was  not  employed  in  its  universal 


1 1 8  The  Syllogism 

signification  in  the  premises  can,  therefore,  be  used  universally 
or  distributively  in  the  conclusion.  This  rule  may  be  violated 
by  using  either  the  major  or  the  minor  term  in  a  wider  sense 
in  the  conclusion  than  in  the  premise  in  which  it  occurs.  The 
resulting  fallacies  are  then  known  as  the  Illicit  Process  of  the 
major  and  minor  terms  respectively.  As  an  illustration  of  the 
illicit  process  of  the  major  term,  we  may  consider  the  following 
argument :  — 

All  rational  beings  are  responsible  for  their  actions, 
Brutes  are  not  rational  beings, 

Therefore  brutes  are  not  responsible  for  their  actions. 
It  will  be  at  once  seen  that  the  major  term, '  beings  responsible 
for  their  actions,'  is  distributed  in  the  conclusion,  but  was  not 
distributed  when  it  appeared  as  the  predicate  of  an  affirmative 
proposition  in  the  major  premise.  The  fallacious  nature  of  this 
argument  may  also  be  shown  by  representing  the  proposition 
by  circles. 

The  illicit  process  of  the  minor  term  is  usually  more  easily 
detected.     We  may  take  as  an  example  of  this  fallacy:  — 

All  good  citizens  are  ready  to  defend  their  country, 

All  good  citizens  are  persons  who  vote  regularly  at  elections, 

Therefore  all  who  vote  regularly  at  elections  are  ready  to  defend 
their  country. 

It  is  clear  that  the  minor  term, '  persons  who  vote  regularly  at 
elections,'  is  undistributed  when  used  as  the  predicate  of  the 
minor  premise.  In  the  conclusion,  however,  it  is  wrongly 
taken  universally,  and  it  is  this  unwarranted  extension  to  which 
the  name  of  illicit  minor  is  given.  Students  are  advised  to 
draw  circles  to  illustrate  the  nature  of  this  fallacy. 


§  30.    The  Rules  of  the  Syllogism  ng 

The  fifth  and  sixth  rules  have  reference  to  negative  premises. 
It  is  not  difficult  to  understand  why  two  negative  premises  can- 
not yield  any  conclusion.  For,  from  the  fact  that  S  and  P  are 
both  excluded  from  M,  we  can  conclude  nothing  regarding 
their  relation  to  each  other.  Two  negative  premises  afford  us 
no  standard  by  means  of  which  we  can  determine  anything  con- 
cerning the  relation  of  major  and  minor  terms.  Again,  where 
one  premise  is  negative  and  the  other  affirmative,  it  is  asserted 
that,  of  the  major  and  minor  terms,  one  agrees,  and  the  other 
does  not  agree,  with  the  middle  term.  The  necessary  inference 
from  these  premises,  then,  is  that  major  and  minor  terms  do 
not  agree  with  each  other.  That  is,  the  conclusion  must  be 
negative. 

It  is  worth  noticing  that  it  is  sometimes  possible  to  obtain  a 
conclusion  from  premises  which  are  both  negative  in  form.  For 
example :  — 

No  one  who  is  not  thoroughly  upright  is  to  be  trusted, 
This  man  is  not  thoroughly  upright, 

Therefore  this  man  is  not  to  be  trusted. 

In  this  example,  although  the  form  of  both  premises  is  negative, 
the  minor  premise  supplies  a  positive  basis  for  argument,  and  is 
really  affirmative  in  character.  Or  we  may  say  that  the  '  not '  in 
the  predicate  of  the  minor  premise  belongs  to  the  predicate,  and 
not  to  the  copula.  The  proposition  may  therefore  be  said  to  affirm, 
rather  than  to  deny. 

The  seventh  and  eighth  rules,  which  refer  to  particular  premises 
can  be  proved  by  considering  separately  all  the  possible  combi- 
nations of  premises.  If  this  is  done,  it  will  be  found  that  these  rules 
are  direct  corollaries  from  the  third  and  fourth,  which  are  con- 
cerned with  the  proper  distribution  of  terms.       It  is  impossible 


120  The  Syllogism 

to  secure  the  necessary  distribution  with  two  particular  premises; 
for  either  the  distribution  of  the  middle  term  will  not  be  provided 
for,  or  if  this  has  been  secured  by  means  of  a  negative  premise, 
the  conclusion  will  show  a  case  of  the  illicit  major  term.  By  means 
of  the  same  rules,  it  may  be  shown  that  a  particular  premise 
always  requires  a  particular  conclusion.  The  truth  of  these 
two  subordinate  canons  also  may  be  readily  shown  by  the  use  of 
circles. 

§  31.  The  Figures  of  the  Syllogism.  — We  have  seen  what 
an  important  part  the  middle  term  plays  in  the  syllogism.  It 
constitutes  the  mediating  link  between  the  major  and  minor 
terms,  and  makes  possible  their  union.  Now  upon  the  position 
of  the  middle  term  in  the  premises  depends  the  Figure  of  the 
syllogism.  There  are  four  possible  arrangements  of  the 
middle  term  in  the  two  premises,  and  therefore  four  figures  of 
the  syllogism.  If  we  let  P  represent  the  major  term,  S  the 
minor,  and  M  the  middle  term,  the  form  of  the  different  fig- 
ures may  be  represented  as  follows :  — 

First  Figure  Second  Figure 

M  — P 
S  — M 


.-.  S  —  P 
Third  Figure 
M  — P 
M  — S 


p- 

-M 

s- 

-M 

.-.  s- 

-P 

Fourth  Figure 

P- 

-M 

M- 

-s 

.-.  s  —  P  .-.  S  — P 

In  the  first  figure,  the  middle  term  is  the  subject  of  the 
major  premise,  and  the  predicate  of  the  minor  premise. 

In  the  second  figure,  the  middle  term  is  predicate  of  both 
major  and  minor  premises. 


§  31-    The  Figures  of  the  Syllogism  121 

The  third  figure  has  the  middle  term  as  the  subject  of  both 
premises. 

In  the  fourth  figure,  the  middle  term  occupies  just  the  oppo- 
site position  in  the  two  premises  to  that  which  it  holds  in 
the  first  figure ;  i.e.  it  is  the  predicate  of  the  major  premise, 
and  the  subject  of  the  minor  premise. 


CHAPTER    IX 

THE   VALID   MOODS    AND   THE    REDUCTION    OF    FIGURES 

§  32.    The  Moods  of  the  Syllogism.  — By  the  Mood  of  a 

syllogism  we  mean  the  combination  of  propositions  A,  E,  I,  and 
O,  which  goes  to  make  it  up.  Thus,  when  a  syllogism  is  made 
up  of  three  universal  affirmative  propositions,  we  speak  of  it 
as  the  mood  AAA;  if  it  is  composed  of  a  universal  negative,  a 
particular  affirmative,  and  a  particular  negative  proposition, 
we  name  it  the  mood  EIO.. 

Every  syllogism,  as  has  been  already  stated,  is  made  up  of 
some  arrangement  of  the  four  propositions  A,  E,  I,  O,  taken 
three  at  a  time.  Now,  there  are  in  all  sixty-four  possible  per- 
mutations of  these  four  propositions  taken  three  at  a  time. 
We  might  then  write  out  these  sixty-four  moods,  and  proceed 
to  determine  which  of  them  are  valid.  But  this  would  be  a 
long  and  somewhat  tedious  undertaking.  Moreover,  if  we 
can  determine  which  are  the  valid  combinations  of  premises, 
we  can  draw  the  proper  conclusions  for  ourselves.  Since, 
then,  there  are  but  two  premises  in  each  syllogism,  we  shall 
have  to  deal  only  with  the  possible  permutations  of  A,  E,  I, 
and  O,  taken  two  at  a  time,  or  with  sixteen  combinations  in 
all. 

The  following,  then,  are  the  only  possible  ways  in  which  the 
propositions  A,  E,  I,  and  O  can  be  arranged  as  premises:  — 


§  33-    The  Special  Canons  of  the  Four  Figures     123 

AA  EA  IA  OA 

AE  EE  IE  OE 

AI  EI  II  OI 

AO  EO  10  00 

Some  of  these  premises,  however,  cannot  yield  conclusions, 
since  they  plainly  violate  certain  rules  of  the  syllogism.  The 
combinations  of  negative  premises  EE,  EO,  OE,  and  OO  can 
be  at  once  struck  out.  Again,  since  no  conclusion  follows  from 
two  particular  premises,  we  can  eliminate  II,  IO,  and  01. 
There  remain,  then,  for  further  consideration  the  combina- 
tions: — 

AA  EA  IA  OA 

AE  —  IE  — 

AI  EI  —  — 

AO  —  — 

At  this  point  we  must  recall  the  fact  that  every  argument 
must  belong  to  one  of  the  four  figures.  We  must  now  there- 
fore ask  this  question:  Which  of  the  above  combinations  of 
premises  will  yield  valid  conclusions  in  the  first,  second,  third, 
and  fourth  figures,  respectively  ?  By  examining  the  form  of 
the  syllogism  in  each  of  these  figures,  we  shall  be  able  to  dis- 
cover what  conditions  must  be  fulfilled  in  each  case,  and  to  lay 
down  special  canons  for  each  figure.  We  shall  first  proceed 
to  state  and  prove  the  special  canons  of  the  different  figures. 
It  will  not,  however,  be  necessary  for  the  student  to  commit 
these  rules  to  memory,  as  he  can  always  derive  them  for  him- 
self by  a  consideration  of  the  form  of  the  argument  in  the 
different  figures. 

§  23-  Tne  Special  Canons  of  the  Four  Figures.  — In  the 
first  figure,  the  minor  premise  must  be  ajjirmative,  and  the  major 
premise  universal. 


124       The    Valid  Moods  and  the  Reduction  of  Figures 
The  first  figure  is  of  the  form:  — 

M  — P 
S  — M 
.\S  —  P 

To  show  that  the  minor  premise  is  affirmative,  we  employ  the 
indirect  method  of  proof.  Let  us  suppose  that  the  minor 
premise  is  not  affirmative,  but  negative.  Then  since  one  prem- 
ise is  negative,  the  conclusion  must  be  negative.  But  if  the 
conclusion  is  a  negative  proposition,  its  predicate,  P,  must  be 
distributed.  Any  term  which  is  distributed  in  the  conclusion 
must,  however,  have  been  distributed  when  it  was  used  in  the 
premise.  P  must  be  distributed,  therefore,  as  the  predicate  of 
the  major  premise.  But  since  negative  propositions  alone 
distribute  their  predicates,  the  major  premise,  M  —  P,  must 
be  negative.  But  by  hypothesis  the  minor  premise,  S  —  M, 
is  negative.  We  have,  therefore,  two  negative  premises, 
which  is  impossible.  Our  supposition,  that  the  minor 
premise  is  negative,  is  therefore  false;  or,  in  other  words,  the 
minor  premise  must  be  affirmative. 

This  having  been  established,  we  can  very  easily  prove  that 
the  major  premise  must  be  universal.  For  the  middle  term, 
M,  must  be  distributed  in  at  least  one  of  the  premises.  But 
it  is  not  distributed  in  the  minor  premise,  for  it  is  there  the 
predicate  of  an  affirmative  proposition.  It  must,  therefore, 
be  distributed  as  the  subject  of  the  major  premise,  that  is,  the 
major  premise  must  be  universal. 

If  we  turn  now  to  the  second  figure,  we  shall  find  that  the 
following  rules  may  be  deduced  from  a  consideration  of  its 
form :  — 


§  33-    The  Special  Canons  of  the  Four  Figures    125 

(1)  One  premise  must  be  negative,  and  the  conclusion  there- 
fore negative. 

(2)  The  major  premise  must  be  universal 
The  second  figure  is  in  the  form:  — 

P— M 

S— M 


.\S— P 

The  reason  for  the  first  rule  is  at  once  evident.  If  one 
premise  is  not  negative,  the  middle  term,  M,  is  not  distrib- 
uted, and  no  conclusion  is  therefore  possible.  The  only 
means  of  securing  distribution  of  the  middle  term  in  the 
second  figure  is  by  means  of  a  negative  premise.  And  if 
one  premise  is  negative,  it  of  course  follows  that  the  conclu- 
sion must  be  negative. 

This  having  been  established,  the  proof  of  rule  2  follows 
almost  immediately.  For,  since  the  conclusion  is  negative, 
its  predicate,  P,  must  be  distributed.  And  since  P  is  distrib- 
uted in  the  conclusion,  it  must  have  been  used  distributively 
when  it  occurred  as  the  subject  of  the  major  premise,  or,  in 
other  words,  the  major  premise  must  be  universal. 

The  third  figure  is  of  the  form :  — 

M— P 

M— S 

.\S—  P 

From  an  analysis  of  this,  the  two  following  rules   may   be 
obtained:  — 

(1)  The  minor  premise  must  be  affirmative. 

(2)  The  conclusion  must  be  particular. 

The  minor  premise  is  here  shown  to   be  affirmative  by 
the  method  employed  in  proving  the  same  rule  in  the  first 


126     The    Valid  Moods  and  the  Reduction  of  Figures 

figure.  That  is,  we  suppose  the  minor  premise  negative 
and  show  that,  as  a  result  of  this  hypothesis,  the  conclusion 
is  negative,  and  the  major  term  distributed.  It  follows, 
then,  that  this  term  must  be  distributed  as  the  predicate 
of  the  major  premise.  But  this  could  happen  only  if  this 
premise  were  negative.  The  hypothesis  that  the  minor 
premise  is  negative  thus  leads  to  the  absurdity  of  two  nega- 
tive premises.  The  conclusion  that  the  opposite  is  true, 
that  the  minor  premise  is  affirmative,  is  therefore  proved 
indirectly. 

Since  the  minor  premise  is  affirmative,  its  predicate 
S  is  undistributed.  This  term  must  therefore  be  used  in 
an  undistributed,  i.e.,  particular  sense  in  the  conclusion. 
And,  as  this  term  forms  its  subject,  the  conclusion  is  par- 
ticular. 

In  the  fourth  figure  the  terms  are  arranged  in  the  follow- 
ing way :  — 

P  — M 

M— S 
,\S—  P 

From  a  consideration  of  the  form  of  this  figure  we  can  obtain 
the  following  special  canons:  — 

(i)  If  either  premise  be  negative,  the  major  premise  must 
be  universal. 

(2)  If  the  major  premise  be  affirmative,  the  minor  must  be 
universal. 

(3)  //  the  minor  premise  be  affirmative,  the  conclusion  must 
be  particular. 

The  student  will  be  able  to  prove  these  canons  for  himself 
by  applying  the  rules  of  the  syllogism  in  the  same  way  as 
has  been  done  in  the  proofs  already  given. 


- 


§  34-    The  Determination  of  the    Valid  Moods     127 

§34.  The  Determination  of  the  Valid  Moods  in  Each  of 
the  Figures.  — We  have  now  to  apply  these  special  canons 
in  order  to  determine  what  moods  are  valid  in  each  of  the 
four  figures.  It  has  already  been  shown  (p.  122)  that  the 
premises  which  are  not  excluded  by  the  general  rules  of  the 
syllogism  are:  — 

AA  EA  IA  OA 

AE  —  IE  — 

AI  EI  —  — 

AO  —  —  — 

Now  we  have  proved  that  in  the  first  figure  the  major  premise 
must  be  universal,  and  the  minor  affirmative.  The  only 
combinations  of  premises  which  will  stand  these  tests  are, 
AA,  EA,  AI,  and  EI.  Drawing  the  proper  conclusion  in 
each  case,  we  have  as  the  four  valid  moods  of  the  first 
figure:  — 

AAA,   EAE,   All,   EIO. 

It  will  be  noticed  that  the  first  figure  enables  us  to  obtain 
as  conclusion  any  one  of  the  four  logical  propositions 
A,  E,  I,  and  O. 

The  special  canons  of  the  second  figure  state  that  the 
major  premise  must  be  universal,  and  one  premise  negative. 
Selecting  the  combinations  of  premises  which  fulfil  these 
conditions,  we  obtain  EA,  AE,  EI,  and  AO.  These  give, 
when  the  conclusions  have  been  drawn,  the  following  four 
moods  of  the  second  figure:  — 

EAE,   AEE,   EIO,   AOO. 

By  means  of  the  second  figure,  therefore,  we  are  able  to 
establish  the  truth  only  of  the  negative  propositions,  E  and  O. 


128      The   Valid  Moods  and  the  Reduction  of  Figures 

In  the  third  figure  the  minor  premise  must  be  affirma- 
tive, and  the  conclusion  particular.  Taking  all  the  com- 
binations in  which  the  minor  is  affirmative,  there  result, 
AA,  IA,  AI,  EA,  OA,  EI.  It  must  be  remembered  that 
the  third  figure  yields  only  particular  conclusions,  even 
where  both  premises  are  universal.  The  valid  moods  in 
this  figure  are  therefore  as  follows:  — 

AAI,  IAI,  All,  EAO,  OAO,  EIO. 

The  canons  of  the  fourth  figure,  which  have  to  do  with 
the  premises,  state  that  where  either  premise  is  negative,  a 
universal  major  is  necessary,  and  that  an  affirmative  major 
premise  must  be  accompanied  by  a  universal  minor.  The 
combinations  of  propositions  which  fulfil  these  conditions 
are  AA,  AE,  IA,  EA,  and  EI.  In  drawing  conclusions 
from  these  premises,  however,  it  is  necessary  to  pay  attention 
to  the  third  canon  of  this  figure,  which  states  that  where 
the  minor  premise  is  affirmative,  the  conclusion  must  be 
particular.  Accordingly,  the  valid  moods  of  this  figure 
may  now  be  written :  — 

AAI,   AEE,   IAI,   EAO,   EIO. 

Here  we  are  able  to  obtain  a  universal  negative  as  a  conclu- 
sion, but  not  a  universal  affirmative.  It  is  interesting  to 
notice  that  the  first  figure  alone  enables  us  to  prove  a  propo- 
sition of  the  form  A. 

It  may  also  be  pointed  out  that  the  combination  [I  E], 
although  not  e^luded  by  the  general  rules  of  the  syllogism, 
cannot  be  used  at  all  as  a  premise,  since  it  violates  the  canons 
of  all  four  figures.  There  remain  in  all,  then,  nineteen 
valid  moods  of  the  syllogism,  —  four  in    the    first  figure, 


§  35-    The  Mnemonic  Lines  129 

four  in  the  second,  six  in  the  third,  and  five  in  the  fourth 
figure. 

§  35.  The  Mnemonic  Lines.  — It  is  not  necessary  to 
commit  to  memory  the  valid  moods  in  each  figure.  By 
applying  the  general  rules  of  the  syllogism  to  the  figure 
in  question,  the  student  will  be  able  to  determine  for  himself 
in  every  case  whether  or  not  an  argument  is  valid.  The 
Latin  Schoolmen  in  the  thirteenth  century,  however,  in- 
vented a  system  of  curious  mnemonic  verses  for  the  pur- 
pose of  rendering  it  easy  to  remember  the  valid  moods 
in  each  figure.  Although  it  is  not  necessary  for  the  student 
to  burden  his  memory  with  these  barbarous  names,  it  is 
interesting  to  understand  the  use  of  the  lines :  — 

Barbara,  Celarent,  Darii,  Ferioque  prions; 
Cesare,  Camestres,  Festino,  Baroko,  secundae; 
Tertia,  Darapti,  Disamis,  Datisi,  Felapton, 
Bokardo,  Ferison,  habet;   Quarta  insuper  addit 
Bramantip,  Camenes,  Dimaris,  Fesapo,  Fresison. 

The  words  printed  in  ordinary  type  are  real  Latin  words, 
indicating  that  the  four  moods  represented  by  Barbara, 
Celarent,  Darii,  and  Ferio  are  the  valid  moods  of  the  first 
figure,  that  the  next  four  are  valid  in  the  second  figure, 
that  the  third  figure  has  six  valid  moods  represented 
by  as  many  artificial  names,  and  that  the  fourth  figure 
adds  five  more.  Each  word  represents  a  mood,  the  vowels 
A,  E,  I,  and  O  indicating  the  quality  and  quantity  of  the 
propositions  which  go  to  compose  them.  Thus,  Barbara 
signifies  the  mood  of  the  first  figure  which  is  made  up  of 
three  universal  affirmative  propositions  AAA;  Cesare,  a 
mood  of  the  second  figure,  composed  of  the  three  proposi- 


130       The    Valid  Moods  and  the  Reduction  of  Figures 

tions  EAE.  These  lines,  then,  sum  up  the  results  reached 
on  pages  126-127  regarding  the  valid  moods  in  each  figure. 
But  certain  consonants  in  these  mnemonic  words  also 
indicate  how  arguments  in  the  second,  third,  or  fourth 
figures  may  be  changed  to  the  form  of  the  first  figure.  The 
first  figure  was  called  by  Aristotle  the  perfect  figure,  and 
the  second  and  third  the  imperfect  figures,  since  he  did  not 
regard  an  argument  in  these  forms  as  so  direct  and  con- 
vincing as  one  of  the  first-mentioned  type.  The  fourth 
figure  was  not  recognized  by  Aristotle,  but  is  said  to  have 
been  introduced  into  logic  by  Galen,  the  celebrated  teacher 
of  medicine,  who  lived  in  the  latter  half  of  the  second  century. 
If  we  consider  an  example  of  this  figure,  the  reason  for  re- 
fusing it  an  equal  rank  with  the  other  three  will  appear:  — 

The  whale  is  a  mammal, 
All  mammals  are  vertebrates, 
Therefore  some  vertebrates  are  whales. 

It  is  plain  that  the  conclusion  of  this  argument  is  some- 
what strained.  That  is,  it  would  be  more  natural  to  obtain 
the  conclusion  '  whales  are  vertebrates,'  than  to  infer  that 
'some  vertebrates  are  whales';  for  this  statement  seems 
to  make  the  species,  or  less  inclusive  term,  the  predicate  of 
the  genus,  or  wider  term.  It  was  for  this  reason,  apparently, 
that  Aristotle  omitted  this  figure,  as  improperly  making 
the  real  major  term  a  minor,  and  the  real  minor  a  major, 
and  so  stating  in  a  less  adequate  way  an  argument  which 
could  have  been  better  formulated  in  the  first  figure. 

The  process  of  changing  an  argument  from  one  of  the 
so-called  imperfect  figures  to  that  of  the  first  figure  is  known 
as    Reduction.     And,   as  we  have  said,  these  curious  but 


§  35-      The  Mnemonic  Lines  131 

ingenious  mnemonic  words  give  rules  for  carrying  out  this 
process.  For  example,  s  indicates  that  the  proposition 
represented  by  the  preceding  vowel  is  to  be  converted  simply. 
Thus  an  argument  in  the  second  figure  of  the  mood  Cesare 
is  changed  to  Celarent  in  the  first  figure,  by  converting  the 
major  premise  simply.  Again,  p  denotes  that  the  preced- 
ing vowel  is  to  be  converted  by  limitation,  or  per  accidens; 
m  is  supposed  to  stand  for  mutare,  and  indicates  that  the 
premises  are  to  be  transposed;  k,  which  is  used  in  the  moods 
Baroko  and  Bokardo,  shows  that  an  indirect  method  of 
proof  or  reduction  is  necessary  to  reduce  the  arguments 
to  the  first  figure. 

Further,  the  initial  consonants  of  the  moods  of  the  imper- 
fect figures  correspond  with  those  of  the  moods  in  the  first 
figures,  to  which  they  can  be  reduced.  Cesare  and  Cames- 
tres  of  the  second  figure,  for  example,  and  Camenes  of  the 
fourth  are  reducible  to  Celarent;  and,  similarly,  Festino,  Felap- 
ton,  Fesapo,  and  Fresison  may  all  be  reduced  to  Ferio. 

The  student  who  understands  the  structure  of  the  syllogism  will 
be  able  to  arrange  an  argument  in  one  figure  or  another,  as  may  be 
most  convenient,  without  the  aid  of  any  mechanical  rules.  It  may 
be  interesting,  however,  to  give  a  single  example  for  the  sake  of 
illustrating  the  workings  of  this  most  ingenious  device.  Let  us  take 
the  following  argument  in  the  second  figure  of  the  mood  AEE,  or 
Camestres :  — 

All  members  of  the  class  are  prepared  for  the  examination, 
No  idle  persons  are  prepared  for  the  examination, 

Therefore  no  idle  persons  are  members  of  the  class. 

Now  the  m  in  Camestres  shows  that  the  major  and  minor  premises 
are  to  be  transposed ;  the  first  s  indicates  that  the  minor  premise  is 


132     The    Valid  Moods  and  the  Reduction  of  Figures 

to  be  converted,  and  the  second  that  the  same  process  must  be 

performed  on  the  conclusion. 

Converting  the  minor  premise  and  transposing,  we  obtain:  — 

No  persons  prepared  for  the  examination  are  idle, 

All  members  of  the  class  are  prepared  for  the  examination. 

Converting  the  conclusion, 

Therefore  no  members  of  the  class  are  idle  persons. 

This  result,  as  will  at  once  be  seen,  is  an  argument  in  the  first 
figure  of  the  mood  EAE,  or  Celarent. 

REFERENCES 

Sir  W.  Hamilton,  Lectures  on  Logic.     Lectures  XX.,  XXI. 
A.  Bain,  Logic,  Part  First,  Deduction,  Bk.  II.,  Ch.  I. 

Note.  —  It  would  be  interesting  to  work  out,  in  connection  with 
the  various  forms  of  inductive  reasoning  treated  in  Part  II.,  the  organic 
relation  of  the  syllogistic  figures,  and  their  natural  applicability  to 
various  purposes  of  argument.  This  task,  however,  seemed  to  lie  beyond 
the  proper  limits  of  this  book.  All  of  the  investigations  on  this  point  start 
from  Hegel's  treatment  in  the  second  part  of  the  Wissenschaft  der  Logik 
(Werke,  Bd.  5,  pp.  115  ff.).  Those  interested  in  this  subject  may  consult 
W.  T.  Harris,  The  Psychologic  Foundations  0/  Education,  Ch.  IX.-XL, 
and  the  same  author's  Logic  oj  Hegel.  See  also  B.  Bosanquet,  Logic, 
Vol.  II.,  pp.  44  ff.,  88  ff.,  and  The  Essentials  oj  Logic,  Lecture  X.;  H.  W.  B. 
Toseph,  An  Introduction  to  Logic,  Ch.  XIV, 


CHAPTER    X 

ABBREVIATED    AND    IRREGULAR    FORMS    OF   ARGUMENT 

§  36.  Enthymemes.  — The  term  '  enthymeme '  seems  to 
have  been  used  by  Aristotle  for  an  argument  from  signs  or 
from  likelihood,  without  complete  proof.  From  this  sense 
of  logical  incompleteness,  the  name  has  come  to  be  applied 
in  modern  times  to  an  argument  in  which  some  part  is  omitted. 
We  have  already  noticed,  in  dealing  with  the  syllogism 
(§  10),  that  one  premise  is  often  omitted.  Indeed,  it  is  but 
seldom  in  ordinary  reasoning  that  we  arrange  our  arguments 
in  the  strict  syllogistic  form.  We  hurry  on  from  one  fact  to 
another  in  our  thinking  without  stopping  to  make  all  the 
steps  definite  and  explicit.  We  feel  it  to  be  a  waste  of  time, 
and  a  trial  to  the  patience,  to  express  what  is  clearly  obvious, 
and  so  we  press  on  to  the  conclusion  which  is,  for  the  time 
being,  the  central  point  of  interest. 

But  the  more  rapid  and  abbreviated  the  reasoning,  the 
more  necessary  is  it  to  keep  a  clear  head,  and  to  under- 
stand what  conclusion  is  aimed  at,  and  what  premises  are 
assumed  in  the  argument.  To  bring  to  light  the  hidden 
assumption  upon  which  an  argument  is  based,  is  often 
the  best  means  of  refuting  it. 

Enthymemes  are  sometimes  said  to  be  of  the  first,  second, 
or  third  order,  according  as  the  major  premise,  the  minor 
premise,  or  the  conclusion  is  wanting.     As  a  matter  of  fact, 


134      Abbreviated  and  Irregular  Forms  of  Argument 

an  enthymeme  of  the  third  order  is  a  rhetorical  device  used 
to  call  special  attention  to  a  conclusion  which  is  perfectly 
obvious,  although  suppressed.  Thus,  for  example,  '  all 
boasters  are  cowards,  and  we  have  had  proofs  that  A  is  a 
boaster.'  Here  the  conclusion  is  at  once  obvious,  and  is 
even  more  prominent  than  if  it  were  actually  expressed. 
It  is  usually  easy  to  complete  an  enthymeme.  If  the 
conclusion  and  one  premise  are  given,  the  three  terms  of 
the  syllogism  are  already  expressed.  For  the  conclusion 
contains  the  major  term  and  the  minor  term;  and  one  of 
these  again,  in  combination  with  the  middle  term,  is  found 
in  the  given  premise.  From  these  data,  then,  it  will  not 
be  difficult  to  construct  the  suppressed  premise.  When 
the  -premises  are  given  without  the  conclusion,  there  is  no 
way  of  determining,  except  from  the  order,  which  is  major 
and  which  is  minor.  It  is  therefore  necessary  to  assume 
that  they  are  already  arranged  in  proper  logical  order,  and 
that  the  subject  of  the  conclusion,  or  minor  term,  is  to  be 
found  in  the  second  premise,  and  the  predicate  of  the  conclu- 
sion, or  major  term,  in  the  first  premise. 

§37.  Prosyllogisms  and  Episyllogisms. — In  deductive 
reasoning  it  is  ofitn  necessary  to  carry  on  the  argument 
through  several  syllogisms,  using  the  conclusion  first  reached 
as  a  premise  in  the  following  syllogism.  For  example,  we 
may  argue:  — 

All  B  is  A 

All  C  is  B 


/.  All  C  is  A. 
But  all  D  is  C 

.'.  All  D  is  A. 


§  37-    Prosyllogisms  and  Episyllogisms  135 

It  is  clear  that  we  have  here  two  arguments  in  the  first 
figure.  The  first  is  called  the  Prosyllogism,  and  the  latter 
the  Episyllogism.  If  the  argument  were  carried  on  further, 
so  as  to  include  three  or  more  syllogisms,  the  second  would 
form  the  Prosyllogism  with  respect  to  the  third,  while  the 
third  would  be  the  Episyllogism  of  the  second.  A  concrete 
example  of  this  kind  of  reasoning  may  now  be  given:  — 

All  timid  men  are  suspicious, 
All  superstitious  men  are  timid, 

Therefore  all  superstitious  men  are  suspicious, 
But  some  educated  men  are  superstitious, 


Therefore  some  educated  men  are  suspicious. 

It  will  be  noticed  that  in  these  examples  the  argument  advances 
from  the  premises  of  the  Prosyllogism,  to  the  conclusion  of  the 
Episyllogism.  It  proceeds,  that  is  to  say,  in  a  forward  direction, 
developing  the  consequences  of  the  premises  which  form  its  starting 
point.  This  mode  of  investigation  is  therefore  called  the  Progres- 
sive ox  Synthetic,  since  it  goes  steadily  forward  building  up  its  results 
as  it  advances.  To  state  the  same  thing  in  different  words,  we  may 
say  that  the  Progressive  or  Synthetic  method  advances  from  the 
conditions  to  what  is  conditioned,  from  causes  to  effects. 

But  it  is  often  necessary  to  proceed  in  the  opposite  way.  We 
have  often  to  go  back  and  show  the  grounds  upon  which  our  prem- 
ises rest,  instead  of  going  forward  to  show  what  consequences 
follow  from  them.  And  when  we  do  this  we  proceed  Regressively 
or  Analytically.  To  take  an  example  which  will  illustrate  both 
ways  of  proceeding :  — 

No  man  is  infallible,  for  no  man  is  omniscient, 
Aristotle  was  a  man, 

Therefore  Aristotle  was  not  infallible. 


136     Abbreviated  and  Irregular  Forms  of  Argument 

In  advancing  from  the  premises  to  the  conclusion  in  this  argument 
our  procedure  is  progressive  or  synthetic.  Instead  of  reasoning  out 
the  consequences  of  the  premises,  however,  we  may  go  back  and 
show  the  grounds  upon  which  the  major  premise  rests.  It  is  evident 
that  this  premise  is  itself  the  conclusion  of  a  syllogism  which  may 
be  expressed  as  follows:  — 

All  infallible  beings  are  omniscient, 

No  man  is  omniscient, 


Therefore  no  man  is  infallible. 
The  regressive  method  goes  backward  from  conclusions  to  premises, 
or  from  the  conditioned  to  its  necessary  conditions.     In  scientific 
investigation  it  reasons  from  effects  to  causes,  while  the  synthetic 
method  advances  from  causes  to  effects. 

§  38.  Sorites,  or  Chains  of  Reasoning.  — A  Sorites  is 
an  abbreviated  form  of  syllogistic  reasoning  in  which  a 
subject  and  predicate  are  united  by  means  of  several  inter- 
mediate terms.  Such  a  train  of  reasoning  represents  sev- 
eral acts  of  comparison,  and  therefore  several  syllogistic 
steps.  But  instead  of  stopping  to  draw  the  conclusion  at 
each  stage,  the  sorites  continues  the  processes  of  compari- 
son, and  only  sums  up  its  results  at  the  close.  We  may 
define  the  sorites,  therefore,  as  a  series  of  prosyllogisms  and 
episyllogisms  in  which  all  of  the  conclusions,  except  the  last, 
are  suppressed.     It  is  usually  stated  in  the  following  form :  — 

All  A  is  B 
All  B  is  C 
All  C  is  D 
All  D  is  E 

.-.  All  A  is  E. 


§  3 8-    Sorites \  or  Chains  of  Reasoning  137 

It  is  evident  that  this  train  of  reasoning  fully  expressed 
is  equivalent  to  the  following  three  syllogisms:  — 
First  Syllogism  Second  Syllogism  Third  Syllogism 

All  B  is  C  All  C  is  D  All  D  is  E 

All  A  is  B  All  A  is  C  (1)  All  A  is  D  (2) 


.-.  AllAisC(i).  .\  All  A  is  D  (2).        .-.  All  AisE  (3). 

There  are  two  rules  to  be  observed  in  using  this  form 
of  the  sorites:  (1)  The  first  premise  may  be  particular,  all  the 
others  must  be  universal ;  (2)  The  last  premise  may  be  neg- 
ative, all  the  others  must  be  affirmative.  It  is  evident 
from  an  examination  of  the  syllogisms  given  above  that  if 
any  premise  except  the  first  were  particular,  the  fallacy 
of  undistributed  middle  would  be  committed.  For,  in  that 
case,  the  middle  term  in  one  of  the  syllogisms  would  be  the 
subject  of  a  particular  proposition,  and  the  predicate  of  an 
affirmative  proposition.  And  if  any  premise  but  the  last 
were  negative,  the  major  term  in  the  syllogism  following 
that  in  which  this  occurred  would  be  distributed  in  the  con- 
clusion without  having  been  distributed  in  the  major  premise. 
We  may  now  give  some  concrete  examples  of  this  kind  of 
reasoning :  — 

Misfortunes  sometimes  are  circumstances  tending  to  improve 
the  character, 

Circumstances  tending  to  improve  the  character  are  promoters 
of  happiness, 

What  promotes  happiness  is  good, 

Therefore  misfortunes  are  sometimes  good. 

In  some  cases  the  different  terms  of  an  argument  of  this 
kind  are  expressed  in  the  form  of  hypothetical  propositions. 


138     Abbreviated  and  Irregular  Forms  of  Argt4tnent 

Thus,  for  example,  we  might  argue:  If  a  man  is  avaricious! 
he  desires  more  than  he  possesses;  if  he  desires  more 
than  he  possesses,  he  is  discontented;  if  he  is  discontented, 
he  is  unhappy;  therefore,  if  a  man  is  avaricious,  he  is 
unhappy.  This  argument  is  hypothetical  in  form  only, 
and  may  be  easily  reduced  to  categorical  type  as  follows:  — 

An  avaricious  man  is  one  who  desires  more  than  he  possesses, 
A  man  who  desires  more  than  he  possesses  is  discontented, 
A  discontented  man  is  unhappy, 

Therefore  an  avaricious  man  is  unhappy. 

It  will  be  noticed  that  the  subject  of  the  first  premise 
in  this  form  of  argument  is  taken  as  the  subject  of  the 
conclusion,  and  that  the  predicate  of  the  conclusion  is  the 
predicate  of  the  last  premise.  This  is  usually  called  the 
Aristotelian  sorites.  But  there  is  another  form  which 
unites  in  the  conclusion  the  subject  of  the  last  premise, 
and  the  predicate  of  the  first,  and  which  is  known  as  the 
Goclenian  sorites.1    This  may  be  thus  represented:  — 

All  A  is  B 
All  C  is  A 
All  D  is  C 
All  E  is  D 


.'.  All  E  is  B. 
Since  B  is  the  predicate  of  the  conclusion,  the  premise  in 
which  it  appears  is  always  to  be  regarded  as  the  major. 
As  a  result  of  this,  it  is  to  be  noticed  that  the  suppressed 
conclusions  in  this  argument  form  the  major  premise  of 
the  following  syllogism,  instead  of  the  minor  premise  as  in 

1  Rudolf  Goclenius  (1547-1628),  Professor  at  Marburg,  first  explained 
this  form  in  his  Isagoge  in  Organum  Aristotlis,  1598, 


§  39-    Irregular  Arguments  139 

the   Aristotelian   sorites.     We  may,  therefore,  expand   the 
reasoning  into  the  three  following  syllogisms:  — 

First  Syllogism  Second  Syllogism  Third  Syllogism 

All  A  is  B  All  C  is  B  All  D  is  B 

All  C  is  A  All  D  is  C  All  E  is  D 


.-.AllCisB.  /.AllDisB.  .\AllEisB. 

A  little  consideration  of  the  form  of  these  syllogisms  will  lead 
the  student  to  see  that  the  rules  given  for  the  Aristotelian 
sorites  must  be  here  reversed.  In  both  forms  of  the  sorites 
there  cannot  be  more  than  one  negative  premise,  nor  more 
than  one  particular  premise.  In  the  Aristotelian  form,  no 
premise  except  the  last  can  be  negative,  and  no  premise 
except  the  first  particular.  In  the  Goclenian  sorites,  on  the 
other  hand,  the  single  premise  which  can  be  negative 
is  the  first,  and  it  is  the  last  alone  which  may  be  particular. 
§  39.  Irregular  Arguments.  — There  are  a  large  number 
of  arguments  employed  in  everyday  life  which  are  valid  and 
convincing,  and  yet  which  cannot  be  reduced  to  the  syllogistic 
form.  The  difficulty  with  these  arguments  is  that  they  appear 
to  have  four  terms,  at  least  in  the  form  in  which  they  are  most 
naturally  stated.  We  may  discuss  such  irregular  forms  of 
reasoning  under  three  headings:  (1)  Arguments  which  deal 
with  the  relations  of  things  in  time  and  space,  or  with  their 
quantitative  determinations;  (2)  arguments  a  fortiori;  (3)  ar- 
guments which  are  largely  verbal  in  character,  and  may  be 
said  to  depend  upon  the  principle  of  substitution. 

(1)  As  an  example  of  the  first  class  of  argument  we  may 
take  the  following :  — 

A  is  greater  than  B, 

B  is  greater  than  C, 

Therefore  A  is  still  greater  than  C. 


£4°      Abbreviated  and  Irregular  Forms  of  Argument 

It  is  obvious  that,  although  we  have  here  four  terms,  the  con 
elusion  is  valid,  and  the  form  of  argument  perfectly  convincing. 
The  truth  seems  to  be  that  in  reasoning  about  quantities  we  do 
not  proceed  upon  the  syllogistic  principle  of  the  inclusion  and 
exclusion  of  terms.  But  knowing  the  continuous  nature  of 
quantity,  we  take  as  our  principle  that,  '  what  is  greater  than 
that  which  is  greater  than  another  is  a  fortiori  greater  than 
that  other.'  It  would  not,  however,  make  the  matter  any 
clearer  to  write  this  as  our  major  premise,  and  bring  the  real 
argument  under  it  in  this  way :  — 

What  is  greater  than  that  which  is  greater  than  another  is 
still  greater  than  that  other, 

A  is  that  which  is  greater  than  that  which  is  greater  than  C, 

Therefore  A  is  still  greater  than  C. 

What  we  have  here  given  as  the  major  premise  is  simply  a 
statement  of  the  nature  of  quantity,  not  a  premise  from  which 
the  conclusion  is  derived.  We  find  the  same  irregularity  in 
arguments  referring  to  the  relations  of  things  in  space  and 
time:  — 

A  is  situated  to  the  east  of  B, 

B  is  situated  to  the  east  of  C, 

Therefore  A  is  to  the  east  of  C. 

In  spite  of  the  formal  deficiency  of  four  terms  the  argument  is 
valid.  It  will  be  observed,  too,  that  it  is  in  virtue  of  the  com- 
parison of  the  position  of  A  and  of  C  with  that  of  B,  that  these 
relative  positions  have  been  determined.  The  principle  upon 
which  we  proceed  may  be  said  to  be  that,  '  what  is  to  the  east 
of  B  is  to  the  east  of  that  which  B  is  to  the  east  of.'  Or  per- 
haps it  would  be  truer  to  fact  to  say  that  we  proceed  in  such 


§  39-    Irregular  Arguments  14 1 

cases  upon  what  wc  know  regarding  the   nature  of  space, 
and  the  relations  of  objects  in  space. 

(2)  A  fortiori  arguments  proceed  to  establish  a  conclu- 
sion by  showing  that  the  facts  and  reasons  which  support  it 
are  more  certain  or  stronger  than  those  which  support  an- 
other conclusion  that  is  unquestioned,  or  generally  accepted. 
They  are  frequent  in  dealing  with  questions  of  time,  space, 
quantity,  and  degrees  of  quality,  and  all  three  of  the  ex- 
amples just  given  may  be  regarded  as  coming  under  this 
head.  In  fact,  we  may  say  that  in  such  matters,  whenever 
the  relation  involved  is  not  one  of  contemporaneousness 
in  time,  coincidence  in  space,  or  equality  in  quantity,  or 
degree  of  quality,  any  argument  naturally  falls  into  the 
a  fortiori  form.  The  reason  for  putting  this  form  into  a  class 
by  itself  is  that  it  is  very  often  employed  outside  of  these  fields. 
To  illustrate  the  two  ways  in  which  it  is  used,  for  proof  and 
disproof  respectively,  let  us  compare  a  possible  argument  ad- 
dressed by  a  vivisectionist  to  a  meat-eater  with  one  urged  upon 
an  anti-vivisectionist  by  a  vegetarian:  — 

(1) 
You  admit  that  it  is  right  to  kill  and  use  animals  for  food, 
This  is  less  needful  than  to  kill  and  use  them  to  discover  the 
causes  and  remedies  of  diseases, 

How  much  more,  then,  should  you  admit  that  vivisection  is  right. 

(2) 
You  do  not  think  that  it  is  right  to  kill  animals  for  vivisection, 
Yet  this  is  more  needful  than  to  kill  them  for  food, 

How  much  less,  then,  should  you  hold  that  it  is  right  to  kill  them 
for  food,  or,  How  much  more  should  you  deny,  etc. 

Such  arguments  as  these  seem  always  to  involve  a  compar- 
ison of  the  grounds  on  which  certain  conclusions  may  be  jus- 


142      Abbreviated  and  Irregular  Forms  of  Argument 

tified,  when  such  grounds  can  be  ranked  in  order  of  logical 
cogency.  In  the  one  case,  it  is  urged  that  since  the  reason  foi 
the  conclusion  advocated  is  stronger  than  one  which  it  is  ad- 
mitted does  establish  a  certain  proposition,  the  conclusion  in 
question  must,  therefore,  be  regarded  as  even  more  firmly  es- 
tablished; in  the  other,  as  the  reason  for  holding  the  principle 
attacked  is  weaker  than  that  which  is  regarded  as  insufficient 
to  justify  another  principle,  it  is  held  that  the  first  principle  is 
still  more  obviously  false  than  that  already  denied,  or  that 
there  is  more  reason  to  deny  it  than  there  is  to  deny  the  other. 
Hence  the  name  argumentum  a  fortiori,  '  argument  from,  or 
by,  the  stronger,'  ('  reason'  being  understood). 

(3)  The  third  class  of  irregular  arguments  is  largely 
verbal  in  character,  and  may  be  dealt  with  very  briefly.  As 
an  example  we  may  consider:  — 

Men  are  willing  to  risk  their  lives  for  gold, 
Gold  cannot  buy  happiness, 

Therefore  men  are  willing  to  risk  their  lives  for  what  cannot  buy 
happiness. 

It  is  doubtful,  I  think,  whether  these  propositions  represent 
any  real  inference.  The  whole  process  may  be  regarded  as  a 
verbal  substitution  in  the  major  premise  of  '  what  cannot  buy 
happiness '  for  the  word  « gold.'  By  a  slight  change  in  the 
form  of  the  proposition,  however,  the  argument  may  be  ex- 
pressed as  a  regular  syllogism  of  the  third  figure:  — 

Gold  is  something  for  which  men  are  willing  to  risk  their  lives, 
Gold  cannot  buy  happiness, 

Therefore  something  which  cannot  buy  happiness  is  something 
for  which  men  are  willing  to  risk  their  lives. 
Another  example  which  also  appears  to  be  irregular  at  first 
sight  is  added:  — 


§  39-    Irregular  Arguments  143 

The  men  of  the  Middle  Ages  were  ready  to  undertake  any  expe- 
dition where  glory  could  be  won, 

The  crusades  were  expeditions  in  which  glory  could  be  won, 

The  crusades,  therefore,  were  readily  undertaken  by  the  men 
of  the  Middle  Ages. 

This  argument  seems  to  be  irregular  in  form  only,  and  by  a 
slight  change  in  form  may  be  expressed  in  the  first  figure:  — 

All  expeditions  in  which  glory  could  be  won  were  readily  under- 
taken by  the  men  of  the  Middle  Ages, 

The  crusades  were  expeditions  in  which  glory  could  be  won, 

Therefore  the  crusades  were  readily  undertaken  by  the  men  of 
the  Middle  Ages. 

REFERENCES, 

Especially  for  §  38 

W.  S.  Jevons,  The  Principles  of  Science,  Introduction. 
F.  H.  Bradley,  The  Principles  of  Logic,  pp.  348-360. 


CHAPTER  XI 

HYPOTHETICAL   AND   DISJUNCTIVE    ARGUMENTS 

§  40.  The  Hypothetical  Syllogism.  —  We  have  hitherto 
been  dealing  with  syllogisms  composed  entirely  of  categori- 
cal propositions,  and  have  not  referred  to  the  use  which  is 
made  of  conditional  propositions  in  reasoning.  A  conditional 
proposition  is  sometimes  defined  as  the  union  of  two  cate- 
gorical propositions  by  means  of  a  conjunction.  It  is  the 
expression  of  an  act  of  judgment  which  does  not  directly  or 
unambiguously  assert  something  of  reality.  We  have  already 
pointed  out  (§  20)  that  there  are  two  classes  of  conditional 
propositions:  the  hypothetical  and  the  disjunctive,  and  corre- 
sponding to  these  we  have  the  hypothetical  and  the  disjunctive 
syllogism.  The  hypothetical  syllogism  has  a  hypothetical 
proposition  as  a  major  premise,  and  a  categorical  proposition 
as  a  minor  premise.  The  disjunctive  syllogism  in  the  same 
way  is  composed  of  a  disjunctive  proposition  as  major,  and 
a  categorical  proposition  as  minor,  premise.  In  addition  to 
these,  we  shall  have  to  treat  of  another  form  of  argument 
called  the  'dilemma,'  which  is  made  up  of  hypothetical  and 
disjunctive  propositions. 

A  hypothetical  proposition  does  not  assert  directly  the  ex- 
istence of  a  fact,  but  states  the  connection  between  a  supposi- 
tion or  condition  and  its  consequence.     It  is  usually  intro- 

144 


§  40.    The  HypotJietical  Syllogism  145 

luced  by  some  word  or  conjunctive  phrase,  like  '  if,'  'supposing,' 
or  'granted  that';  as,  e.g., '  if  he  were  to  be  trusted,  we  might 
give  him  the  message';  'suppose  that  A  is  B,  then  C  is  D.' 
The  part  of  a  hypothetical  proposition  which  expresses  the 
supposition  or  condition  is  known  as  the  Antecedent;  the 
clause  stating  the  result  is  called  the  Consequent.  Thus,  in 
the  proposition,  'he  would  write  if  he  were  well,'  the  consequent, 
'he  would  write,'  is  stated  first,  and  the  antecedent,  '  if  he  were 
well,'  follows. 

The  hypothetical  syllogism,  as  has  been  already  remarked, 
has  a  hypothetical  proposition  as  its  major,  and  a  categorical 
proposition  as  its  minor,  premise:  — 

If  justice  is  to  prevail,  his  innocence  will  be  proved, 
And  justice  will  prevail, 

Therefore  his  innocence  will  be  proved. 

It  will  be  noticed  that  in  this  argument  the  minor  premise 
affirms  the  antecedent,  and  that,  as  a  result,  the  conclusion 
affirms  the  consequent.  This  form  is  known  as  the  construc- 
tive hypothetical  syllogism,  or  the  modus  ponens. 

In  the  following  example  it  will  be  observed  that  the  con- 
sequent is  denied,  and  the  conclusion  obtained  is  therefore 

negative. 

If  he  were  well,  he  would  write, 

He  has  not  written, 


Therefore  he  is  not  well. 


This  is  called  the  destructive  hypothetical  syllogism,  or  modus 
tollens. 

The  rule  of  the  hypothetical  syllogism  may  therefore  be 
stated  as  follows:    Either  affirm   the  antecedent  or  deny  the 


146  Hypothetical  and  Disjunctive  Arguments 

consequent.  If  we  affirm  the  antecedent,  i.e.,  declare  that  the 
condition  exists,  the  consequent  necessarily  follows.  And,  on 
the  other  hand,  if  the  consequent  is  declared  to  be  non-existent, 
we  are  justified  in  denying  that  the  condition  is  operative. 

The  violation  of  these  rules  gives  rise  to  the  fallacies  of 
denying  the  antecedent,  and  of  affirming  the  consequent.  Thus, 
for  example,  we  might  argue :  — 

If  he  were  well,  he  would  write, 
But  he  is  not  well, 


Therefore  he  will  not  write. 
Here  the  antecedent  is  denied,  and  the  argument  plainly  false. 
For  we  cannot  infer  that  his  being  well  is  the  only  condition 
under  which  he  would  write.  We  do  not  know,  in  other  words, 
that  the  antecedent  stated  here  is  the  only,  or  essential  condition 
of  the  consequent.  We  know  that  if  there  is  fire,  there  must 
be  heat;  but  we  cannot  infer  that  there  is  no  heat  when  no  fire 
is  present.  Of  course,  if  we  can  be  certain  that  our  antecedent 
expresses  the  essential  condition,  or  real  sine  qua  non  of  the 
consequent,  we  can  go  from  the  denial  of  the  former  to  that  of 
the  latter.     For  example:  — 

If  a  triangle  is  equilateral,  it  is  also  equiangular, 
This  triangle  is  not  equilateral, 

Therefore  it  is  not  equiangular. 
Usually,  however,  when  the  hypothetical  form  of  expression  is 
employed,  we  cannot  be  certain  that  the  antecedent  expresses 
the  sole,  or  essential  condition,  of  the  consequent.  At  the 
ordinary  stages  of  knowledge  we  have  to  content  ourselves 
with  reasoning  from  antecedent  conditions,  without  being  able 
to  show  that  no  other  condition  is  possible. 


§  4°-    T1'ie  Hypothetical  Syllogism  147 

To  illustrate  the  fallacy  of  affirming  the  consequent,  we  may 
take  the  following  example :  — 

If  perfect  justice  prevailed,  the  rich  would  not  be  permitted  to 
rob  the  poor, 

But  the  rich  are  not  permitted  to  rob  the  poor, 

Therefore  perfect  justice  prevails. 

Here  it  will  be  noticed  that  the  consequent  states  only  one 
result  of  the  prevalence  of  '  perfect  justice.'  Because  the 
consequent  is  declared  to  exist,  it  by  no  means  follows  that  it 
exists  as  a  consequence  of  the  operation  of  this  condition.  It 
is  also  worth  noting  in  this  example  that  the  consequent  of 
the  major  premise  is  negative.  The  minor  premise  which 
affirms  the  consequent  also  takes  a  negative  form.  To  deny 
the  consequent  we  should  have  to  say,  '  the  rich  are  permitted 
to  rob  the  poor.'  Or,  to  put  the  matter  generally,  it  is  nec- 
essary to  remember  that  the  affirmation  of  a  negative  propo- 
sition is  expressed  by  a  negative  proposition,  and  that  the 
denial  of  a  negative — the  negation  of  a  negation — is,  of 
course,  positive  in  form. 

A  type  of  hypothetical  argument  differing  in  form  from  the 
hypothetical  syllogism  is  that  in  which  premises  and  conclusion 
are  all  hypothetical  propositions,  as,  for  example :  — 

If  the  tariff  is  increased,  prices  will  rise, 

If  prices  rise,  the  majority  of  the  people  will  be  discontented, 
If  the  majority  are  discontented,  the  Republican  party  will  be 
defeated  at  the  next  election, 

Therefore,  if  the  tariff  is  increased,  the  Republican  party  will 
be  defeated  at  the  next  election. 


148  Hypothetical  and  Disjunctive  Arguments 

This  is  an  hypothetical  sorites,  corresponding  to  the  Aristotelian 
form  of  the  categorical  sorites,  in  that  its  conclusion  unites  the  ante- 
cedent of  the  first  premise  with  the  consequent  of  the  last.  There 
are  also  hypothetical  sorites  which  unite  the  antecedent  of  the  last 
premise  with  the  consequent  of  the  first  in  their  conclusion,  and 
thus  correspond  to  the  Goclenian  sorites.  Such  sorites  are  often 
hypothetical  in  form  only,  as  has  been  pointed  out  in  the  preceding 
chapter,  and  when  this  is  the  case  they  may  be  reduced  to  cate- 
gorical syllogisms  of  the  first  figure,  as  in  the  example  there 
given  (§38). 

§  41.  Relation  of  Categorical  and  Hypothetical  Argu- 
ments. —  It  is  evident  that  the  form  of  the  hypothetical 
syllogism  is  very  different  from  that  of  the  categorical.  But, 
although  this  is  the  case,  it  must  not  be  supposed  that  with  the 
former  we  have  passed  to  a  new  and  wholly  distinct  type  of 
reasoning.  In  hypothetical  reasoning,  as  in  categorical,  it  is 
the  presence  of  a  universal  principle  which  enables  us  to  bring 
into  relation  two  facts  which  formerly  stood  apart.  Indeed,  in 
many  cases,  it  is  a  matter  of  indifference  in  which  form  the 
argument  is  stated.  Thus,  we  may  argue  in  hypothetical 
form :  — 

If  a  man  is  industrious,  he  will  be  successful, 

A  is  an  industrious  man, 


Therefore  A  will  be  successful. 

The  same  argument  may,  however,  be  expressed  equally  well 
in  categorical  form :  — 

All  industrious  men  will  be  successful, 
A  is  an  industrious  man, 


Therefore  A  will  be  successful. 


§  41-    Categorical  and  Hypothetical  Arguments     1 49 

ft  is  clear  that,  in  spite  of  the  different  forms  in  which  the 
argument  is  expressed,  the  reasoning  is  essentially  the  same  in 
both  cases.  The  middle  term,  or  general  principle  which 
makes  it  possible  to  unite  the  subject  and  predicate  of  the  con- 
clusion, in  the  hypothetical  as  well  as  in  the  categorical 
syllogism,  is  '  industrious.'  A  will  be  successful,  we  argue, 
because  he  is  industrious,  and  it  is  a  rule  that  industrious  men 
are  successful. 

Moreover,  if  an  argument  is  fallacious  in  one  form,  it  will 
also  be  fallacious  when  expressed  in  the  other.  The  defects  of 
an  argument  cannot  be  cured  simply  by  a  change  in  its  form. 
When  an  hypothetical  argument,  in  which  the  antecedent  is 
denied,  is  expressed  categorically,  we  have  the  fallacy  of  the 
illicit  major  term.  Thus,  to  state  the  example  of  denying  the 
antecedent  given  on  page  146,  we  get:  — 

The  case  of  his  being  well  is  a  case  of  his  writing, 
The  present  is  not  a  case  of  his  being  well, 

Therefore  the  present  is  not  a  case  of  his  writing. 

Similarly,  when  an  argument  in  which  the  consequent  is 
affirmed  is  changed  to  the  categorical  form,  the  defect 
in  the  reasoning  appears  as  the  fallacy  of  undistributed 
middled  — 

If  this  tree  is  an  oak,  it  will  have  rough  bark  and  acorns, 
This  tree  has  rough  bark  and  acorns, 

Therefore  it  is  an  oak. 

When  this  argument  is  expressed  in  categorical  form,  it  is  at 
once  clear  that  the  middle  term  is  not  distributed  in  either  the 
major  or  minor  premise :  — 


150  Hypotlietical  and  Disjunctive  Arguments 

All  oak  trees  are  trees  having  rough  bark  and  acorns, 
This  tree  is  a  tree  having  rough  bark  and  acorns, 

Therefore  this  tree  is  an  oak. 

The  change  from  the  categorical  to  the  hypothetical  form 
of  argument,  then,  does  not  imply  any  essential  change  in  the 
nature  of  the  reasoning  process  itself.  Nevertheless,  it  is 
important  to  note  that  hypothetical  propositions  and  hypothet- 
ical arguments  emphasize  one  aspect  of  thinking,  which  is 
entirely  neglected  by  the  theory  of  the  categorical  syllogism. 
When  dealing  with  the  extension  of  terms  (§  16),  we  pointed 
out  that  every  term,  as  actually  used  in  a  proposition,  has  both 
an  extensive  and  an  intensive  function.  That  is,  the  terms  of 
a  proposition  are  employed  both  to  name  certain  objects  or 
groups  of  objects,  and  to  connote  or  imply  certain  attributes 
or  qualities.  In  the  proposition,  '  these  are  oak  trees,'  the 
main  purpose  is  to  identify  the  trees  given  in  perception  with 
the  class  of  oak  trees.  When,  on  the  other  hand,  we  say, '  igno- 
rant people  are  superstitious,'  the  proposition  does  not  refer 
directly  to  any  particular  individuals,  but  states  the  necessary 
connection  between  ignorance  and  superstition.  Although 
the  existence  of  ignorant  persons  who  are  also  superstitious  is 
presupposed  in  the  proposition,  its  most  prominent  function  is 
to  assert  a  connection  of  attributes  which  is  wholly  impersonal. 
We  may  perhaps  say  that,  in  spite  of  the  categorical  form, 
the  proposition  is  essentially  hypothetical  in  character.  Its 
meaning  might  very  well  be  expressed  by  the  statement, '  if  a 
man  is  ignorant,  he  is  also  superstitious.'  What  is  here  em- 
phasized is  not  the  fact  that  ignorant  persons  exist,  and  are 
included  in  the  class  of  superstitious  persons,  but  rather  the 
general  law  of  the  necessary  connection  of  ignorance  and 


§  41-    Categorical  and  Hypothetical  Arguments     151 

superstition.  The  existence  of  individuals  to  whom  the  latf 
applies  is,  of  course,  presupposed  by  the  proposition.  It  is 
not,  however,  its  main  purpose  io  directly  affirm  their 
existence. 

We  have  reached,  then,  the  following  position:  Every 
judgment  has  two  sides,  or  operates  in  two  ways.  On  the 
one  hand,  it  asserts  the  existence  of  individual  things,  and  sets 
forth  their  qualities  and  relations  to  other  things.  But,  at  the 
same  time,  every  judgment  seeks  to  go  beyond  the  particular 
case,  and  to  read  off  a  general  law  of  the  connection  of  attri- 
butes or  qualities  which  shall  be  true  universally.  In  singular 
and  particular  propositions,  the  categorical  element  —  the 
direct  assertion  of  the  existence  of  particular  objects  —  is 
most  prominent,  although  even  here  the  hint  or  suggestion  of 
a  general  law  is  not  altogether  absent.  When  we  reach  the 
universal  proposition,  however,  the  reference  to  particular 
things  is  much  less  direct,  and  the  meaning  seems  capable  of 
expression  in  hypothetical  form. 

Now  in  the  chapters  on  the  categorical  syllogism  this  latter 
aspect  of  judgments  has  been  left  out  of  account.  Proposi- 
tions were  there  interpreted  as  referring  directly  to  objects,  or 
classes  of  objects  (cf.  §  23).  The  proposition,  S  is  P,  for 
example,  was  taken  to  affirm  that  some  definite  object,  or  class 
of  objects,  S,  falls  within  the  class  P.  And  the  fact  that  it  is 
possible  to  apply  this  theory  shows  that  it  represents  one  side 
of  the  truth.  But  the  student  must  sometimes  have  felt  that, 
in  this  procedure,  the  most  important  signification  of  the  prop- 
osition is  lost  sight  of.  It  seems  absurd  to  say,  for  example, 
that  in  the  proposition,  *  all  material  bodies  gravitate,'  the  class 
of  'material  bodies'  is  included  in  the  wider  class  of  'things 
that  gravitate.'    The  main  purpose  of  the  judgment  isevidently 


•52  Hypothetical  and  Disjunctive  Arguments 

to  affirm  the  necessary  connection  of  the  attributes  of  materi 
ality  and  gravitation.  The  judgment  does  not  refer  directly 
to  things,  or  classes  of  things  at  all,  but  asserts  without  imme- 
diate reference  to  any  particular  object,  if  material,  then  gravi- 
tating. The  propositions  of  geometry  are  still  more  obviously 
hypothetical  in  character.  '  The  three  angles  of  a  triangle  are 
equal  to  two  right  angles,'  for  example,  cannot,  without 
violence,  be  made  to  mean  that  the  subject  is  included  in  the 
class  of  things  which  are  equal  to  two  right  angles.  The  main 
purpose  of  the  proposition  is  obviously  to  assert  the  necessary 
connection  of  the  'triangularity'  and  the  equality  of  angles 
with  two  right  angles,  and  not  to  make  any  direct  assertion 
regarding  any  actually  existing  object  or  group  of  objects. 

We  reach,  then,  the  following  conclusion:  Our  thought 
is  at  once  both  categorical  and  hypothetical.  As  categori- 
cal, it  refers  directly  to  objects  and  their  relations.  The 
terms  of  the  proposition  are  then  taken  in  extension  to 
represent  objects  or  groups  of  objects,  and  the  copula  to 
assert  the  inclusion  of  the  subject  in  the  predicate,  or,  in 
cases  of  negative  propositions,  to  deny  this  relation.  As 
hypothetical,  the  reference  to  things  is  much  more  indirect. 
The  terms  of  the  proposition  are  no  longer  regarded  as 
representing  objects  or  classes,  but  are  interpreted  from 
the  point  of  view  of  intension.  The  judgment  affirms  or 
denies  the  connection  of  the  qualities  or  attributes  connoted 
by  the  terms,  and  not  that  of  the  objects  which  they  denote. 
Sometimes  the  one  aspect  of  thought,  sometimes  the  other, 
is  the  more  prominent. 

In  sense-perception  and  in  simple  historical  narra- 
tion, assertions  are  made  directly  and  categorically  regard- 
ing things  and  events.    The  main  interest  is  in  particular 


§  41-    Categorical  and  Hypothetical  Arguments      153 

objects,  persons,  or  events,  and  our  judgments  refer  directly 
and  unambiguously  to  them.  But,  as  we  have  already 
seen,  our  thought  from  its  very  beginning  attempts  to  get 
beyond  the  existence  of  particular  things  and  events,  and  to 
discover  what  qualities  of  objects  are  necessarily  connected. 
We  pass  from  perception  and  observation  to  explanation, 
from  the  narration  of  events,  to  the  discovery  of  the  law  of 
their  connection.  And,  as  a  result  of  this  advance,  our 
judgments  deal  no  longer  exclusively  with  particular  objects 
and  events,  and  the  fact  of  their  relation,  but  with  the  gen- 
eral laws  of  the  connection  between  attributes  and  qualities. 
There  is,  of  course,  no  fixed  point  at  which  we  pass  from 
the  categorical  to  the  hypothetical  aspect  of  thinking.  But, 
in  general,  as  we  pass  from  judgments  of  sense-percep- 
tion and  memory,  to  a  statement  of  theories  and  laws, 
the  hypothetical  element  comes  more  and  more  clearly 
into  the  foreground.  We  have  seen  that  it  is  almost  impos- 
sible to  interpret  propositions  regarding  geometrical  rela- 
tions as  referring  directly  to  classes  of  objects.  In  the  same 
way,  it  is  evident  that  propositions  which  state  general 
laws  are  more  truly  hypothetical  than  categorical.  When 
we  assert  that  'all  men  are  mortal,'  the  proposition  does 
not  intend  to  state  a  fact  in  regard  to  each  and  every  man,  or 
to  refer  directly  to  individuals  at  all,  but  to  express  the  essen- 
tial and  necessary  relation  between  humanity  and  mortality. 
A  proposition  which  is  essentially  hypothetical  in  character 
may  then  be  expressed  in  categorical  form.  It  must  be 
remembered  that  it  is  not  the  form,  but  the  purpose  or  func- 
tion of  a  proposition,  which  determines  its  character.  The 
hypothetical  form,  however,  does  justice  to  an  aspect  of 
thought    which    is    especially    prominent    in    the    universal 


154  Hypothetical  and  Disjunctive  Arguments 

laws  and  formulas  of  scientific  knowledge,  and  which  is 
not  adequately  represented  by  the  theory  of  subsumption, 
or  the  inclusion  of  the  subject  in  the  predicate. 

§  42.  Disjunctive  Arguments.  — A  disjunctive  proposi- 
tion, as  we  have  already  seen,  is  of  the  form,  'A  is  either 
B,  or  C,  or  D';  a  triangle  is  either  right-angled,  obtuse- 
angled,  or  acute-angled.  It  is  sometimes  said  to  be  the 
union  of  a  categorical  and  a  hypothetical  proposition.  On 
the  one  hand,  it  asserts  categorically  regarding  A,  and  with- 
out reference  to  any  external  condition.  But  the  disjunctive 
proposition  is  not  simple  like  the  categorical  proposition: 
it  states  its  results  as  a  series  of  related  conditions  and  con- 
sequences. If  A  is  not  B,  it  tells  us,  it  must  be  either  C  or 
D;  and  if  it  is  C,  it  follows  that  it  cannot  be  B  or  D. 

A  disjunctive  proposition  may  at  first  sight  appear  to  be 
a  mere  statement  of  ignorance,  and,  as  such,  to  be  less 
useful  than  the  simple  categorical  judgment  of  perception. 
And  it  is  true  that  the  disjunctive  form  may  be  employed  to 
express  lack  of  knowledge.  '  I  do  not  know  whether  this 
tree  is  an  oak  or  an  ash  ';  '  he  will  come  on  Monday  or  some 
other  day.'  A  true  disjunctive  proposition,  however,  is 
not  a  mere  statement  of  ignorance  regarding  the  presence 
or  absence  of  some  fact  of  perception.  It  is  an  attempt,  on 
the  part  of  intelligence,  to  determine  the  whole  series  of 
circumstances  or  conditions  within  which  any  fact  of  percep- 
tion may  fall,  and  to  state  the  conditions  in  such  a  way 
that  their  relations  are  at  once  evident.  And  to  do  this 
implies  positive  knowledge.  In  the  first  place,  the  enumera- 
tion of  possibilities  must  be  exhaustive,  no  cases  must  be 
overlooked,  and  no  circumstances  left  out  of  account.  Sec- 
ondly, the  members  of  the  proposition  must  be  taken  so  as 


§  42.    Disjunctive  Arguments  1 55 

to  be  really  disjunctive.  That  is,  they  must  be  exclusive  of 
one  another.  We  cannot  combine  disjunctively  any  terms 
we  please,  as  '  perhaps  this '  or  '  perhaps  that.'  But  it  is  only 
when  we  understand  the  systematic  connections  of  things  in 
the  field  in  question,  that  we  are  able  to  express  these  con- 
nections in  the  form,  either  B  or  C,  and  thus  assert  that  the 
presence  of  one  excludes  the  other. 

A  disjunctive  proposition,  then,  presupposes  systematic 
knowledge,  and  is  consequently  the  expression  of  a  com- 
paratively late  stage  in  the  evolution  of  thought.  It  is 
true  that  disjunction  may  involve  doubt  or  ignorance  regard- 
ing any  particular  individual.  We  may  not  be  able  to  say 
whether  A  is  B  or  C  or  D.  But,  before  we  can  formulate 
the  disjunctive  proposition,  we  must  be  already  acquainted 
with  the  whole  set  of  possible  conditions,  and  also  with  the 
relation  in  which  those  conditions  stand  to  one  another. 
Our  knowledge,  when  capable  of  being  formulated  in  the 
disjunctive  major  premise  of  an  argument,  is  so  exhaustive 
and  systematic,  that  the  application  to  a  particular  case 
effected  by  the  minor  premise  appears  almost  as  a  tautology. 
This  will  be  evident  in  the  disjunctive  arguments  given  below. 

There  are  two  forms  of  the  disjunctive  syllogism.    The 

first  is  sometimes  called  the  modus  tollendo  ponens,  or  the 

mood    which    affirms    by    denying.    The    minor    premise, 

that  is,  is  negative,  and  the  conclusion  affirmative.    The 

form  is,  — 

A  is  either  B  or  C, 

A  is  not  C, 

Therefore  A  is  B. 
The  negative  disjunctive  argument    has   an    affirmative 
minor  premise.     It  is  known  as  the  modus  ponendo  tollens, 


156  Hypothetical  and  Disjunctive  Arguments 

or  the  form  which,  by  affirming  one  member  of  the  disjunc 
*ive  series,  denies  the  others,  — 

A  is  B  or  C  or  D, 
But  A  is  B, 


Therefore  A  is  neither  C  nor  D. 


It  is,  of  course,  a  very  simple  matter  to  draw  the  con- 
clusion from  the  premises  in  these  cases.  As  we  have 
already  indicated,  the  real  intellectual  work  consists  in 
obtaining  the  premises,  especially  in  discovering  the  re- 
lations enumerated  in  the  major  premise.  It  is  in  formu- 
lating the  major  premise,  too,  that  errors  are  most  likely  to 
arise.  As  already  pointed  out,  it  is  essential  that  the  dis- 
junctive members  shall  be  exhaustively  enumerated,  and  also 
that  they  shall  exclude  one  another.  But  it  is  not  always 
easy  to  discover  all  the  possibilities  of  a  case,  or  to  formu- 
late them  in  such  a  way  as  to  render  them  really  exclusive. 
If  we  say,  '  he  is  either  a  knave  or  a  fool,'  we  omit  the  possi- 
bility of  his  being  both  the  one  and  the  other  to  some  extent. 
A  great  many  statements  which  are  expressed  in  the  form  of 
disjunctive  propositions  are  not  true  logical  disjunctives. 
Thus  we  might  say,  '  every  student  works  either  from  love  of 
learning,  or  from  love  of  praise,  or  for  the  sake  of  some 
material  reward.'  But  the  disjunction  does  not  answer 
the  logical  requirements ;  for  it  is  possible  that  two  or  more 
of  these  motives  may  influence  his  conduct  at  the  same 
time.  The  disjunctive  members  are  neither  exclusive  nor 
completely  enumerated. 

§  43.  The  Dilemma.  — A  dilemma  is  an  argument  which 
includes  all  possible  assertions  about  its  subject-matter 
under  the  head  of  alternatives  that    involve   further   con- 


§  43-    The  Dilemma  157 

sequences,  so  that  part  or  all  of  these  consequences  must 
be  admitted  whichever  alternative  be  allowed.  In  other 
words,  '  a  dilemma  is  a  compound  hypothetical  syllogism, 
partly  disjunctive  in  form.'  The  major  premise  is  always 
hypothetical,  and  the  disjunction  is  usually  stated  in  the 
minor  premise.  As  the  word  is  used  in  ordinary  life,  we 
are  said  to  be  in  a  dilemma  whenever  there  are  but  two 
courses  of  action  open  to  us,  and  when  both  of  these  have 
unpleasant  consequences.  In  the  same  way,  the  logical 
dilemma  when  used  controversially  shuts  an  opponent  in 
to  a  choice  between  alternatives,  either  of  which  leads  to  a 
conclusion  he  would  gladly  avoid. 

The  first  form,  which  is  sometimes  called  the  Simple  Construc- 
tive Dilemma,  yields  a  simple  or  categorical  conclusion :  — 

If  A  is  B,  C  is  D ;  and  if  E  is  F,  C  is  D, 
But  either  A  is  B,  or  E  is  F, 


Therefore  C  is  D. 

It  will  be  noticed  that  the  minor  premise  affirms  disjunc- 
tively the  antecedents  of  the  two  hypothetical  propositions 
which  form  the  major  premise,  and  that  the  conclusion 
follows  whichever  alternative  holds.  We  may  take  as  a 
concrete  example  of  this  type  of  argument:  — ■ 

If  a  man  acts  in  accordance  with  his  own  judgment,  he  will  be 
criticised ;  and  if  he  is  guided  by  the  opinions  and  rules  of  others, 
he  will  be  criticised, 

But  he  must  either  act  in  accordance  with  his  own  judgment,  ol 
be  guided  by  the  opinions  of  others, 

Therefore,  in  any  case,  he  will  be  criticised. 


158  Hypothetical  and  Disjunctive  Arguments 

The  Simple  Destructive  Dilemma  also  yields  a  categorical 
conclusion.  But  in  this  form  of  the  dilemma,  the  major 
premise  has  one  antecedent  and  two  consequents,  and  these 
consequents  are  denied  in  the  minor  premise.  The  ante- 
cedent is  therefore  denied  in  the  conclusion.  A  famous 
example  is  the  argument  of  Zeno  to  show  that  it  is  against 
reason  to  believe  that  motion  really  takes  place:  — 

If  a  thing  moves,  it  must  move  either  in  the  place  where  it  is 
or  in  the  place  where  it  is  not, 

But  it  cannot  move  where  it  is,  nor  can  it  move  where  it  is  not, 

Therefore  it  cannot  move- 
It  is  worth  noticing  that  in  this  example  the  minor  premise 
is  not  disjunctive;  that  is,  it  denies  the  consequents  of  the 
major  premise  together,  and  not  disjunctively.  All  the 
disjunction  here  is  in  the  second  part  of  the  major  premise. 
The  Simple  Destructive  Dilemma  is  the  only  form  in  which 
this  occurs,  and  the  disjunction  may  be  in  the  minor  premise 
in  this  form  also. 

The  hypothetical  propositions  which  make  up  the  major 
premise  of  a  dilemma  do  not  usually  have  the  same  ante- 
cedent or  consequent,  as  is  the  case  in  the  examples  just 
given.  When  the  antecedents  and  consequents  involved 
are  different,  the  dilemma  is  said  to  be  complex,  and  the 
conclusion  has  the  form  of  a  disjunctive  proposition.  In 
the  Complex  Constructive  Dilemma,  the  minor  premise 
affirms  disjunctively  the  antecedents  of  the  major,  and  the 
conclusion  is  consequently  affirmative.  We  may  take,  as  an 
example,  the  argument  by  which  the  Caliph  Omar  is  said 
to  have  justified  the  burning  of  the  Alexandrian  library:  — 


§  43-    The  Dilemma  159 

If  these  books  contain  the  same  doctrines  as  the  Koran,  thej 
are  unnecessary;  and  if  they  are  at  variance  with  the  Koran,  they 
are  wicked  and  pernicious, 

But  they  must  either  contain  the  same  doctrines  as  the  Koran 
or  be  at  variance  with  it, 


Therefore  these  books  are  either  unnecessary  or  wicked  and 
pernicious. 

A  fourth  form,  the  Complex  Destructive  Dilemma,  obtains 
a  conclusion  made  up  of  two  negations  disjunctively  related, 
by  denying  disjunctively  the  consequents  of  the  hypothetical 
propositions  that  form  the  major  premise  of  the  argument. 
We  may  take  the  following  example:  — 

If  an  officer  does  his  duty,  he  will  obey  orders ;  and  if  he  is 
intelligent,  he  will  understand  them, 

But  this  officer  either  disobeyed  his  orders,  or  else  he  misun- 
derstood them, 


Therefore,  he  either  did  not  do  his  duty,  or  else  he  is  not 
intelligent, 

By  taking  more  than  two  hypothetical  propositions  as 
major  premise,  we  may  obtain  a  Trilemma,  a  Tetralemma, 
or  a  Polylemma.  These  forms,  however,  are  used  much 
less  frequently  than  the  Dilemma. 

The  dilemma  is  essentially  a  polemical  or  controversial 
form  of  argument.  Its  object,  when  so  used,  as  we  have 
stated,  is  to  force  an  unwelcome  conclusion  upon  an  adver- 
sary by  confining  him  to  a  choice  between  two  alternatives, 
either  of  which  necessarily  leads  to  such  a  conclusion.  We 
sometimes  speak  of  the  horns  of  the  dilemma,  and  of  our 
adversary  as  'gored,'  whichever  horn  he  may  choose.     Di- 


160  HypotJietical  atid  Disjunctive  Arguments 

lemmas,  however,  like  all  controversial  arguments,  are  more 
often  fallacious  than  valid.  The  minor  premise  of  a  dt 
lemmatic  argument,  as  we  have  already  seen,  is  a  disjunc- 
tive proposition  with  two  members.  But  it  is  very  rarely 
that  two  alternatives  exhaust  all  the  possible  cases.  The 
cases  enumerated,  too,  may  not  exclude  each  other,  or  be 
real  alternatives  at  all.  The  dilemma  is  thus  subject  to  all 
the  dangers  which  we  have  already  noticed  in  the  case  of 
the  disjunctive  argument.  In  the  minor  premise,  in  addition, 
it  is  necessary  to  see  that  the  canon  of  the  hypothetical 
syllogism,  'affirm  the  antecedent  or  deny  the  consequent,' 
is  observed.  If  this  rule  is  not  obeyed,  the  logical  form  of 
the  argument  will  not  be  valid. 

A  dilemmatic  argument  may  be  attacked  in  three  ways,  the 
traditional  names  for  which  are  continuations  of  the  metaphor 
of  the  'horns.' 

(i)  One  may  'escape  between  the  horns.'  This  is  simply  to 
point  out  that  the  alternatives  presented  in  the  minor  premise 
are  not  exhaustive,  and  that  there  are  one  or  more  other  possi- 
bilities left  unmentioned. 

(2)  The  dilemma  may  be  'taken  by  the  horns.'  That  is,  one 
may  accept  the  alternative  antecedents  proposed  as  exhaustive, 
but  deny  that  one  or  both  of  the  consequents  asserted  really  follow 
from  them.     For  an  example,  let  us  take  this  argument:  — 

If  we  have  trusts,  prices  will  be  excessive;  and  if  we  do  not 
have  them,  our  manufacturing  industries  will  fail  to  meet  foreign 
competition, 

But  we  must  either  have  trusts  or  not  have  them, 

Therefore  either  prices  will  be  excessive  or  our  manufacturing 
industries  will  fail  to  meet  foreign  competition. 


§  43-    The  Dilemma  161 

One  might  reply  to  this  either  by  denying  that  there  is  any 
inevitable  connection  between  trusts  and  excessive  prices,  or  by 
denying  that  trusts  are  necessary  to  enable  us  to  compete  with 
foreign  firms. 

(3)  Sometimes,  as  a  reply  to  a  defective  dilemma,  a  counter- 
dilemma  is  proposed,  leading  to  an  exactly  opposite  conclusion. 
When  this  is  done,  the  original  dilemma  is  said  to  be  'rebutted.' 
Whenever  such  an  opposition  is  possible,  each  of  the  two  dilemmas 
by  itself  fails  to  state  exhaustively  either  the  possible  antecedents, 
or  else  the  consequents  following  from  the  given  antecedents. 
Formal  rebuttal,  therefore,  is  rather  a  rhetorical  device  for  showing 
up  the  weakness  of  an  opponent's  position,  than  a  logical  argu- 
ment for  the  direct  proof  of  one's  own  conclusion. 

A  classical  example  of  such  rebuttal  is  the  famous  Litigiosus. 
Protagoras  the  sophist  is  said  to  have  made  an  agreement  to  teach 
Euathlus  the  art  of  pleading  for  a  fee,  one-half  of  which  was  to  be 
paid  to  him  when  he  was  fully  instructed,  and  the  other  half  when  he 
won  his  first  case  in  court.  Euathlus  put  off  beginning  his  prac- 
tice, and  Protagoras  finally  brought  suit  for  the  other  half  of  his  fee. 
Protagoras  offered  the  following  argument  in  his  own  behalf:  — 

If  Euathlus  loses  this  case,  he  must  pay  me,  by  the  judgment  of 
the  court ;  and  if  he  wins  it,  he  must  pay  me  in  accordance  with  the 
terms  of  his  contract, 

But  he  must  either  lose  it  or  win  it, 

Therefore  he  must  pay  me  in  any  case. 

Euathlus  then  offered  the  following  rebuttal:  — 

If  I  win  the  case,  I  ought  not  to  pay,  by  the  judgment  of  the  court ; 
and  if  I  lose  it,  I  ought  not  to  pay,  by  the  terms  of  the  contract, 
But  I  must  either  win  it  or  lose  it, 

Therefore  I  ought  not  to  pay. 

The  onesidedness  of  dilemmas  which  directly  confront  each  other 


1 62  HypotJietical  and  Disjunctive  Arguments 

in  this  fashion  is  evident  in  this  example.  For  a  complete  statement 
of  the  case,  the  major  premises  of  both  should  be  combined.  There 
are  really  two  points  of  view,  or  standards  of  reference,  involved 
in  each  alike  —  the  expected  judgment  of  the  court,  and  the  terms 
of  the  contract.  Protagoras  states  the  consequent  of  his  first  ante- 
cedent in  accordance  with  the  first  standard,  and  the  consequent 
of  the  second  antecedent  in  accordance  with  the  second  standard. 
Euathlus  simply  reverses  the  application  of  the  standards.  But 
both  disputants  make  use  of  the  two  standards  alternately,  when  one 
only  can  really  be  applied.  Either  the  literal  terms  of  the  contract 
must  be  observed,  and  in  that  case  there  can  be  no  judgment  of  the 
court  at  all,  since  the  proper  ground  of  action  —  i.e.  Euathlus  hav- 
ing won  his  first  suit  —  is  not  present.  The  suit  must  simply  be  dis- 
missed. Or  else,  if  a  judgment  in  equity  is  to  be  granted,  and  the 
contract  interpreted  in  accordance  with  its  spirit  and  intention,  and 
not  with  its  letter,  the  appeal  is  to  the  judgment  of  the  court  on  the 
whole  case  presented,  and  this  judgment  will  be  either  for  or 
against  Euathlus.  There  is,  therefore,  no  real  dilemma  involved 
in  the  circumstances  at  all,  the  appearance  of  it  in  each  argument 
being  due  to  the  presence  of  two  contradictory  points  of  view. 

All  dilemmas  related  in  this  way  of  direct  opposition,  using  prem- 
ises of  the  same  terms,  will  be  found  to  involve  a  similar  neglect  of 
some  aspect  of  the  situation ;  and  this  is  why  we  have  said  that  a 
dilemma  in  rebuttal,  while  a  striking  rhetorical  device  for  attacking 
an  opponent's  position,  does  nothing  to  establish  the  truth  of  one's 
own.  Indeed,  if  the  rebutting  dilemma  be  allowed  to  remain  un- 
supported by  any  further  argument,  it  may  be  considered  as  pre- 
sumptive proof  that  neither  party  to  the  debate  has  any  right  to  a 
positive  conclusion  in  the  matter.  Another  and  simpler  example 
may  make  this  clearer :  — 

If  a  man  is  single,  he  is  unhappy  because  he  has  no  one  to  take 
care  of  him,  and  if  he  is  married,  he  is  unhappy  because  he  has  to 
take  care  of  a  wife.     (Major  premise  of  original.) 


§  43-    The  Dilemma  163 

If  a  man  is  married,  he  is  happy  because  he  has  a  wife  to  take 
care  of  him ;  and  if  he  is  single,  he  is  happy  because  he  has  no  one 
to  take  care  of.     (Major  premise  of  rebutting  dilemma.) 

Here,  as  in  the  former  example,  the  vague  and  shifting  use  of 
any  standard  of  reference  is  apparent  in  both  the  original  and 
the  rebutting  dilemma.  There  is  no  attempt  to  define  terms,  or 
to  bring  the  differen;  standards  into  relation;  the  argument 
moves  and  has  its  being  in  the  mere  limbo  of  undefined  phrases 
where  it  seems  possible  to  prove  anything,  just  because  it  is  pos- 
sible to  prove  nothing. 

REFERENCES 

Especially  for  §  40 

J.  S.  Mill,  Logic,  Bk.  I.,  Ch.  V. 
C.  Sigwart,  Logic,  Pt.  I.,  Ch.  VII. 

W.  Minto,  Logic  Inductive  and  Deductive,  pp.  129-138,  and  pp 
214-225. 

F.  H.  Bradley,  The  Principles  of  Logic,  Bk.  I.,  Ch.  II. 

B.  Bosanquet,  The  Essentials  of  Logic,  Lecture  VI. 

(On  §  42)  H.  W.  B.  Joseph,  An  Introduction  to  Logic,  pp.  330-337. 

W.  R.  Boyce  Gibson,  The  Problem  of  Logic,  pp.  271-277,  292-295. 


CHAPTER    Xn 

FALLACIES    OF   DEDUCTIVE   REASONING 

§  44.  Classification  of  Fallacies.  — A  Fallacy  may  be 
defined  as  a  conclusion  or  interpretation,  resulting  from 
processes  of  thinking  which  claim  to  be  valid,  but  which 
fail  to  conform  to  the  requirements  of  logic.  Various  other 
terms,  like  'Sophism,'  'Paralogism,'  etc.,  are  employed  as 
more  or  less  exact  synonyms.  We  shall  hereafter  treat  of 
the  fallacies  or  errors  to  which  inductive  reasoning  is  most 
subject  (Ch.  XX.).  At  present,  however,  it  is  necessary  to 
consider  the  fallacies  which  are  likely  to  attend  the  employ- 
ment of  the  syllogistic  form  of  reasoning.  In  considering 
the  subject,  we  shall  find  that  many  fallacies  belong  equally 
to  both  kinds  of  reasoning.  This  is  especially  true  of  errors 
which  arise  from  the  careless  use  of  words. 

The  first  systematic  account  of  fallacies  was  given  in 
Aristotle's  treatise,  On  Sophistical  Difficulties  (trepl  <ro$i<r- 
tik6>v  iXeyxcov).  In  this  work,  Aristotle  divides  fallacies 
into  two  classes:  those  which  are  due  to  language  (irapa 
rr}v  \ei;Lv,  or,  as  they  are  usually  called,  fallacies  in  dictione) , 
and  those  which  are  not  connected  with  language  (e£&>  tt}? 
Xe£e&>?,  extra  dictionem).  Under  the  first  head,  he  enu- 
merates six  kinds  of  fallacies,  and  under  the  second,  seven. 
Aristotle's  principle  of  classification  is,  however,  not  entirely 
satisfactory.  We  must  try  to  find  some  positive  principle 
or  principles  of  classification  which  will  render  us  more 
assistance  in  understanding  the  relations  between  the  vari- 

164 


§  44-    Classification  of  Fallacies  165 

ous  fallacies  than  is  afforded   by  Aristotle's  division  into 
those  which  belong  to  language,  and  those  which  do  not. 

In  the  strict  sense  of  the  word,  a  fallacy  is  to  be  denned 
as  an  error  in  reasoning.  In  the  syllogism,  however,  propo- 
sitions or  premises  form  the  data  or  starting-point.  If, 
now,  these  propositions  are  not  properly  understood,  the 
conclusions  to  which  they  lead  are  likely  to  be  false.  We 
may  then  first  divide  fallacies  into  Errors  of  Interpretation, 
and  Fallacies  in  Reasoning.  Errors  in  interpreting  propo- 
sitions might,  perhaps,  be  more  properly  treated  in  a  work 
on  rhetoric  than  in  a  chapter  on  logical  fallacies.  But  it 
has  been  the  custom  ever  since  the  time  of  Aristotle  to 
include  in  the  enumeration  of  logical  fallacies  a  number  of 
errors  which  are  likely  to  arise  in  interpreting  propositions. 
Moreover,  as  we  saw  in  Chapter  VII.,  there  are  certain 
processes  of  interpretation,  like  Obversion  and  Conversion, 
which  are  sometimes  called  immediate  inference,  and  which 
require  a  knowledge  of  the  logical  structure  of  proposi- 
tions. 

The  Fallacies  which  arise  in  the  process  of  reasoning, 
we  may  again  divide  into  Formal  Fallacies,  or  violations 
of  the  syllogistic  rules,  and  Material  Fallacies.  The  latter 
class  may  be  further  divided  into  Fallacies  of  Equivocation 
(including  Ambiguous  and  Shifting  Terms,  Composition, 
Division,  Accident,  and  the  Dilemmatic  Fallacy),  and  Fal- 
lacies of  Presumption  (including  Petitio  Principii,  Irrele- 
vant Conclusion,  Non  Sequitur,  and  Complex  Questions). 
The  following  table  will  summarize  this  classification:  — 


1 66 


Fallacies  of  Deductive  Reasoning 


Fallacies 

rial 

1 

Errors  in  Interpretation 
(i)    Illogical  Obversion  or 

1 
Mistakes  in  Reasonn 

Conversion 

(2)  Amphiboly 

(3)  Accent 

Forn 

wl 

1 
Mate 

.1 
Equivocation 

1     . 
Presumption 

In  Categorical 
Arguments 

(I) 

(2) 

(3) 
(4) 

(5) 

Four  Terms 
Undistributed 

Middle 
Illicit  Major 
Illicit  Minor 
Negative 
Premises 

(1)  Ambiguous 

and  Shifting 
Terms 

(2)  Composition 

(3)  Division 

(4)  Accident 

(5)  Dilemmatic 

Fallacy 

(?) 

00 
(3) 
(4) 

Petitio    Prin- 

cipii 
Complex 

Question 
Irrelevant 

Conclusion 
Non  Sequitur 

In 

Hypothetical  - 
Arguments 
In  Disjunctive 

A,-rri,rr.0ntc      \ 

(6) 
(7) 

(8) 

Denying  the  Antecedent 
Affirming  the  Consequent 

Imperfect  Disjunction 

Arguments 


§  45.  Errors  in  Interpretation.  — This  class  of  fallacies 
results  from  imperfect  understanding  of  the  meaning  of 
propositions.  They  are  not,  then,  strictly  speaking,  errors 
of  reasoning  at  all.  If,  however,  the  propositions  employed 
as  premises  in  an  argument  are  not  correctly  understood, 
the  conclusions  founded  upon  them  are  likely  to  be  erroneous. 
And  even  if  the  proposition,  which  is  wrongly  interpreted, 
is  not  made  the  basis  of  further  reasoning,  it  is  in  itself  the 
result  of  an  intellectual  error  against  which  it  is  possible 
to  guard.  We  do  not,  of  course,  profess  to  point  out  all 
the  possible  sources  of  error  in  interpreting  propositions. 
The  only  rule  applicable  to  all  cases  which  can  be  given  is 
this:  Accept  no  proposition  until  you  understand  its  exact 
meaning,  and  know  precisely  what  it  implies.     Deliberation 


§  45-    Errors  in  Interpretation  167 

and  attention,  both  with  regard  to  our  own  statements 
and  those  of  others,  are  the  only  means  of  escaping  errors 
of  this  kind. 

(1)  Illogical  Obversion  or  Conversion.  — In  a  previous 
chapter  (Ch.  VII.),  we  have  treated  of  Obversion,  Con- 
version, Contraposition,  etc.,  and  shown  the  rules  to  be 
followed  in  stating  the  obverse  or  the  converse  of  a  propo- 
sition. In  Obversion,  we  interpret  or  show  what  is  involved 
in  a  proposition,  by  stating  its  implications  in  a  proposition 
of  the  opposite  quality.  And  unless  we  have  clearly  grasped 
the  meaning  of  the  original  proposition,  mistakes  are  likely 
to  arise  in  changing  from  the  affirmative  to  the  negative 
form  of  statement,  or  from  the  negative  to  the  affirmative. 
Thus,  we  should  fall  into  an  error  of  this  kind  if  we  should 
take  the  proposition,  '  honesty  is  always  good  policy,'  to  be 
the  equivalent  of,  or  to  imply,  the  statement,  '  dishonesty 
is  always  bad  policy.'  Nor  can  we  obtain  by  obversion 
the  proposition,  '  all  citizens  are  allowed  to  vote,'  from, 
'  no  aliens  are  allowed  to  vote.' 

In  Conversion,  we  take  some  proposition,  A  is  B,  and 
ask  what  assertion  it  implies  regarding  the  predicate.  Does 
'  all  brave  men  are  generous  '  imply  also  that  '  all  generous 
men  are  brave '  ?  This  is,  perhaps,  the  most  frequent 
source  of  error  in  the  conversion  of  propositions.  I  do  not 
mean  that  in  working  logical  examples  we  are  likely  to  con- 
vert proposition  A  simply,  instead  of  by  limitation.  But 
in  the  heat  of  debate,  or  when  using  propositions  without 
proper  attention,  there  is  a  natural  tendency  to  assume 
that  a  proposition  which  makes  a  universal  statement 
regarding  the  subject  does  the  same  with  regard  to  the  pred- 
icate.    And,  although  such  errors  are  very  obvious  when 


1 68  Fallacies  of  Deductive  Reasoning 

pointed  out,  — as,  indeed,  is  the  case  with  nearly  a!l  logical 
fallacies,  — they  may  very  easily  impose  upon  us  when  our 
minds  are  not  fully  awake,  that  is,  when  attention  is  not 
active  and  consciously  on  guard,  or  when  they  occur  in 
the  midst  of  a  long  and  complicated  argument.  Of  the 
other  methods  of  interpretation  perhaps  contraposition  is 
most  likely  to  be  a  source  of  error.  We  have  already  (§  28) 
given  the  rules  for  obtaining  the  contrapositive  of  any  propo- 
sition. Some  practice  in  working  examples  will  enable  one 
to  perceive  readily  what  is  the  logical  contrapositive  to  any 
proposition,  and  what  forms  are  fallacious. 

(2)  Amphiboly,  or  amphibology  (afMJ>if3o\ia) ,  consists 
in  misconception  arising  from  the  ambiguous  grammatical 
construction  of  a  proposition.  A  sentence  may  have  two 
opposite  meanings,  but  one  may  be  more  natural  and  prom- 
inent than  the  other.  A  deception  may  be  practised  by 
leading  a  person  to  accept  the  meaning  more  strongly  sug- 
gested, while  the  significance  intended  is  the  very  opposite, 
as,  e.g.  '  I  hope  that  you  the  enemy  will  slay.'  In  Shake- 
speare's Henry  VI.,  we  have  an  instance  of  amphiboly  in  the 
prophecy  of  the  spirit,  that  "  the  Duke  yet  lives  that  Henry 
shall  depose."  Many  of  the  famous  utterances  of  the 
ancient  oracles  were  of  this  character,  as  the  reported  answer 
to  Crcesus  when  he  inquired  at  Delphi:  "  If  Crcesus  should 
wage  war  against  the  Persians,  he  would  destroy  a  mighty 
empire."  The  more  ambiguous  the  oracle,  the  more  read- 
ily it  could  be  explained  in  accordance  with  the  event,  which 
in  this  case  was  the  destruction  of  the  empire  of  Crcesus. 

(3)  The  Fallacy  of  Accent  is  a  misconception  due  to  the 
accent  or  emphasis  being  placed  upon  the  wrong  words  ir. 
a  sentence.     It  may,  therefore,  be  regarded  as  a  rhetorical 


§  45-    Errors  in  Interpretation  169 

rather  than  as  a  logical  fallacy.  Jevons's  examples  of 
this  fallacy  may  be  quoted  in  part.  "  A  ludicrous  instance 
is  liable  to  occur  in  reading  Chapter  XIII.  of  the  First  Book 
of  Kings,  verse  27,  where  it  is  said  of  the  prophet,  'And  he 
spake  to  his  sons,  saying,  Saddle  me  the  ass.  And  they 
saddled  him.'  The  italics  indicate  that  the  word  him  was 
supplied  by  the  translators  of  the  authorized  version,  but  it 
may  suggest  a  very  different  meaning.  The  command- 
ment, '  Thou  shalt  not  bear  false  witness  against  thy  neigh- 
bour,' may  be  made  by  a  slight  emphasis  of  the  voice  on 
the  last  word  to  imply  that  we  are  at  liberty  to  bear  false 
witness  against  other  persons.  Mr.  De  Morgan,  who  remarks 
this,  also  points  out  that  the  erroneous  quoting  of  an  author, 
by  unfairly  separating  a  word  from  its  context,  or  itali- 
cizing words  which  were  not  intended  to  be  italicized,  gives 
rise  to  cases  of  this  fallacy."  !  Jevons  is  also  authority  for 
the  statement  that  Jeremy  Bentham  was  so  much  afraid 
of  being  led  astray  by  this  fallacy  that  he  employed  a  person 
to  read  to  him  whose  voice  and  manner  of  reading  were 
particularly  monotonous. 

But  these  misinterpretations  of  single  propositions  are 
comparatively  trivial  instances  of  this  fallacy.  In  a  broader 
sense,  the  fallacy  appears  in  connected  arguments  of  any 
kind  in  which,  while  the  facts  are  not  actually  misstated, 
certain  aspects  of  them  are  so  disproportionately  dwelt 
upon  and  emphasized,  at  the  expense  of  the  rest,  that  a  false 
idea  of  the  subject  in  its  entirety  is  the  result.  In  this 
wider  form,  this  fallacy  is  one  that  may  be  described  as  the 
particular  vice  of  special  pleading;  and  the  caution  that 
may  be  suggested   against  it   is,   in   the  language  of  thp 

1  Jevons,  Lessons  in  Logic,  p    1 74. 


170  Fallacies  of  Deductive  Reasoning 

astronomer,  to  make  allowances  for  the  '  personal  equation ' 
both  in  one's  own  thinking  and  in  that  of  others. 

§  46.  Formal  Fallacies.  —  We  shall  follow  our  table, 
and  deal  with  mistakes  of  Reasoning  under  the  two  head- 
ings of  Formal  Fallacies,  and  Material  Fallacies.  Formal 
fallacies  arise  from  violations  of  the  rules  of  the  syllogism. 
The  breaches  of  these  rules  have  been  already  pointed  out 
and  illustrated  in  our  discussion  of  the  various  forms  of 
syllogistic  argument.  The  analysis  of  arguments,  with  a 
view  to  the  detection  of  such  fallacies,  where  any  exist,  is 
a  very  important  exercise,  and  affords  valuable  mental 
discipline.  It  seems  only  necessary  here  to  add  a  remark 
regarding  the  first  fallacy  on  our  list,  that  of  Four  Terms,  or 
Quatemio  Terminorum,  as  it  is  usually  called  by  logicians. 

The  first  canon  of  the  categorical  syllogism  states  that 
'  a  syllogism  must  contain  three  and  only  three  terms.' 
This  rule  would  of  course  be  violated  by  such  an  argument  as, 

Frenchmen  are  Europeans, 
Englishmen  are  Anglo-Saxons, 


Therefore  Englishmen  are  Europeans. 

It  is  so  obvious  that  this  example  does  not  contain  a  real 
inference  that  no  one  would  be  likely  to  be  misled  by  the 
pretence  of  argument  which  it  contains.  In  some  cases, 
however,  a  term  may  be  used  in  two  senses,  although  the 
words  by  which  it  is  expressed  are  the  same.  The  following 
example  may  be  given:  — 

Every  good  law  should  be  obeyed, 
The  law  of  gravitation  is  a  good  law, 

Therefore  the  law  of  gravitation  should  be  obeyed- 


§  47-    Material  Fallacies  171 

Here  we  have  really  four  terms.  The  word  '  law,'  in  the 
first  proposition,  means  a  command  given  or  enactment 
made  by  some  persons  in  authority.  A  'good  law'  in  this 
sense  then  means  a  just  law,  or  one  which  has  beneficial 
results.  But  in  the  second  proposition  it  signifies  a  state- 
ment of  the  uniform  way  in  which  phenomena  behave 
under  certain  conditions.  A  '  good  law  '  from  this  point  of 
view  would  imply  a  correct  statement  of  these  uniformities. 
It  is  interesting  to  note  that  this  example  may  also  be  re- 
garded as  an  instance  of  Equivocation,  and  classified  as  a 
case  of  an  ambiguous  middle  term.  It  is  often  possible 
to  classify  a  fallacy  under  more  than  a  single  head. 

There  are,  however,  cases  where  an  argument  may  seem 
at  first  sight  to  have  four  terms,  but  where  the  defect  is 
only  verbal.  The  matter  must,  of  course,  be  determined  by 
reference  to  the  meaning  of  terms  and  not  merely  to  the 
verbal  form  of  expression.  It  is  ideas  or  concepts,  and 
not  a  form  of  words,  which  are  really  operative  in  reasoning. 

§  47.  Material  Fallacies.  — What  are  called  material 
fallacies  do  not  result  from  the  violation  of  any  specific 
logical  rules.  They  are  usually  said  to  exist,  not  in  the 
form,  but  in  the  matter  of  the  argument.  Consequently, 
it  is  sometimes  argued,  the  detection  and  description  of 
them  do  not  properly  belong  to  logic  at  all.  We  have 
found,  however,  that  all  these  fallacies  have  their  source 
in  Equivocation  and  Presumption.  They  thus  violate 
two  of  the  fundamental  principles  of  logical  argument. 
For  all  logical  reasoning  presupposes  that  the  terms  em- 
ployed shall  be  clearly  defined,  and  used  throughout  the 
argument  with  a  fixed  and  definite  signification.  And, 
secondly,  logic  requires   that   the  conclusion  shall   not  be 


1 72  Fallacies  of  Deductive  Reasoning 

assumed,  but  derived  strictly  from  the  premises.  The 
violation  of  these  principles  is,  therefore,  a  proper  mattel 
of  concern  to  the  logician.  We  shall  treat  first  of  the  falla- 
cies of  Equivocation. 

(A)  The  fallacies  of  Equivocation  have  been  enumerated 
as  Ambiguous  and  Shifting  Terms,  Composition,  Division, 
and  Accident.  These  all  result  from  a  lack  of  clearness 
and  definiteness  in  the  terms  employed.  We  shall  deal 
with  them  briefly  in  order. 

(1)  The  phrase,  Ambiguous  and  Shifting  Terms,  describes 
the  first  fallacy  of  this  group.  A  special  case  of  it  appears 
in  the  Fallacy  of  Ambiguous  Middle.  It  is  obvious  that  the 
middle  term  cannot  form  a  proper  standard  of  comparison, 
if  its  meaning  is  uncertain  or  shifting.  A  standard  of  meas- 
ure must  be  fixed  and  definite.  One  illustration  of  this 
case  of  the  fallacy  will  be  sufficient:  — 

Partisans  are  not  to  be  trusted, 
Democrats  are  partisans, 


Therefore  Democrats  are  not  to  be  trusted. 

The  middle  term,  '  partisan,'  is  evidently  used  in  two  senses 
in  this  argument.  In  the  first  premise  it  signifies  persons 
who  are  personally,  or  with  undue  bias,  interested  in  some 
cause  ;  and  in  the  latter  it  simply  denotes  the  members  of  a 
political  party. 

But  either  the  Minor  or  the  Major  Terms  of  a  syllogism 
may  also  be  ambiguous  as  well  as  the  Middle,  and  be  used 
in  a  different  sense  in  the  conclusion,  than  they  are  in  their 
respective  premises.  One  example  of  ambiguity  in  the 
Major  term  may  be  given:  — 


§  47-    Material  Fallacies  1 73 

What  is  not  forbidden  by  law,  no  one  has  a  right  to  prevent  my 
doing. 

Reprinting  the  works  of  foreign  authors  is  not  forbidden  by 

law. 


Therefore,  no  one  has  a  right  to  prevent  me  from  reprinting 
such  works. 

Here  '  right '  in  the  major  premise  means  '  legal  right ' 
and  in  the  conclusion  '  moral  right';  '  prevent '  in  the  major 
premise  implies  restraint  by  force  or  penalty,  if  necessary, 
but  in  the  conclusion  it  is  used  to  mean  the  use  of  any  means 
of  restraint  whatever.  The  use  of  the  word  '  right '  in 
various  meanings  is  a  frequent  source  of  such  fallacies, 
and  the  comment  of  J.  S.  Mill  on  it  might  well  be  read  by 
the  student.1 

It  is  often  the  case,  especially  where  the  major  or  the  minor 
term  is  concerned,  that  this  fallacy  cannot  be  perpetrated 
without  some  verbal  change  in  the  terms,  which,  however, 
is  made  plausible  by  some  similarity  in  the]words  employed. 
Aristotle  described  some  of  the  ways  in  which  such  shifts  in 
meaning  are  frequently  disguised  under  the  name  of  the 
Fallacy  of  Figure  of  Speech.  Words  which  have  the  same 
roots  may  sometimes  be  substituted  one  for  another,  though 
they  have  taken  on  different  meanings;  as,  for  example, 
the  noun  '  presumption,'  the  verb  '  presume,'  and  the  adjec- 
tive '  presuming.'  Or  we  may  get  a  wrong  meaning  for  a 
word  from  its  having  a  similar  inflection  with  other  words 
of  different  meaning.  An  example  of  this  is  the  passage 
in  which  J.  S.  Mill  argues  that  as  what  is  seen  is  visible,  and 
what  is  heard  is  audible,  so  what  is  desired  must  be  desirable 

1  Cf.  System  of  Logic,  Bk.  V.,  Ch.  VII.,  §  I. 


174  Fallacies  of  Deductive  Reasoning 

—-  therefore  morally  good.  But  desirable  means  primarily 
not  what  is  or  can  be,  but  what  ought  to  be  desired. 

Then,  again,  as  Archbishop  Whately  points  out,  this 
fallacy  may  be  committed  by  using  a  term  at  one  time 
in  its  usual  meaning,  and  at  another  in  its  strict  etymo- 
logical sense.  Thus,  he  remarks,  it  is  frequently  argued 
from  the  strict  original  meaning  of  '  represent,'  that  a  rep- 
resentative in  the  legislature  is  merely  the  spokesman  of  his 
constituents,  and  has  no  right  to  use  his  independent  judg- 
ment in  his  voting  or  public  utterances.  Such  reasoning,  it  is 
obvious,  does  not  necessarily  prove  anything;  for  the  orig- 
inal meaning  of  a  term  may  be  widely  different  from  the 
true  nature  and  proper  functions  of  the  things  and  per- 
sons to  which  it  later  comes  to  be  applied. 

But  trivial  as  such  merely  verbal  argument  may  seem 
when  exposed,  it  is  often  a  source  of  confusion.  Thus  a 
lawyer,  for  example,  might  pass  from  a  proper  insistence  on 
following  the  original  intention  and  meaning  in  interpret- 
ing the  words  of  a  statute,  to  the  mistaken  attempt  to  deter- 
mine how  a  new  law  should  be  framed  by  considering  what 
the  accepted  name  of  the  things  to  which  it  is  to  apply  meant 
when  it  was  first  used.  And  when  an  argument  is  long, 
and  is  not  arranged  in  syllogistic  form,  fallacies  of  this  kind 
are  much  more  difficult  of  detection  than  in  the  simple 
examples  which  have  been  given.  It  is  of  the  utmost  im- 
portance, then,  to  insist  on  realizing  clearly  in  consciousness 
the  ideas  for  which  each  term  stands,  and  not  to  content 
ourselves  with  following  the  words. 

(2)  The  fallacy  of  Composition  arises  when  we  affirm  some- 
thing to  be  true  of  a  whole,  which  holds  true  only  of  one  or 
more  of  its  parts  when  taken  separately  or  distributively. 


§  47-    Material  Fallacies  175 

Sometimes  the  error  is  due  to  confusion  between  the  distribu- 
tive and  collective  signification  of  '  all,'  as  in  the  following 
example:  — 

All  the  angles  of  a  triangle  are  less  than  two  right  angles, 
A,  B,  and  C  are  all  the  angles  of  this  triangle, 

Therefore  A,  B,  and  C  are  less  than  two  right  angles. 

It  is,  of  course,  obvious  that  '  all  the  angles  of  a  triangle ' 
in  the  major  premise  signifies  each  and  every  angle  when 
taken  by  itself,  and  that  the  same  words  in  the  minor  prem- 
ise signify  all  the  angles  collectively.  What  is  true  of  all 
the  parts  taken  separately,  is  not  necessarily  true  of  the 
whole.  We  cannot  say  that  because  no  one  member  of  a 
jury  is  very  wise  or  very  fair-minded,  the  jury  as  a  whole 
are  not  likely  to  bring  in  a  just  verdict.  The  members 
may  mutually  correct  and  supplement  each  other,  so  that 
the  finding  of  the  jury  as  a  whole  will  be  much  fairer  and 
wiser  than  the  judgment  of  any  single  individual  composing 
it.  Another  instance  of  this  fallacy  which  is  often  quoted 
is  that  by  which  protective  duties  are  sometimes  supported :  — 

The  manufacturers  of  woollens  are  benefited  by  the  duty  on 
woollen  goods;  the  manufacturers  of  cotton  by  the  duty  on  cotton; 
the  farmer  by  the  duties  on  wool  and  grain ;  and  so  on  for  all  the 
other  producing  classes;  therefore,  if  all  the  products  of  the  country 
were  protected  by  an  import  duty,  all  the  producing  classes  would 
be   benefited   thereby. 

But,  because  each  class  would  be  benefited  by  an  import 
tax  upon  some  particular  product,  it  does  not  necessarily 
follow  that  the  community  as  a  whole  would  be  benefited, 
if  all  products  were  thus  protected.     For,   obviously,   the 


176  Fallacies  of  Deductive  Reasoning 

advantages  which  any  class  would  obtain  might  be  more 
than  offset  by  the  increased  price  of  the  things  which  they 
would  have  to  buy.  On  the  other  hand,  it  would  be  neo 
essary  to  take  into  consideration  the  fact  that  an  increase 
in  the  prosperity  of  one  class  indirectly  brings  profit  to  all 
the  other  members  of  the  same  society.  We  cannot  regard 
a  whole  as  simply  a  sum  of  parts,  but  must  consider  also 
the  way  in  which  the  parts  act  and  react  upon  one  another. 
(3)  The  fallacy  of  Division  is  the  converse  of  Composition. 
It  consists  in  assuming  that  what  is  true  of  the  whole  is  also 
true  of  the  parts  taken  separately.  Some  term,  which  is 
used  in  the  major  premise  collectively,  is  employed  in  a 
distributive  sense  in  the  minor  premise  and  conclusion. 
The  following  example  will  illustrate  this:  — 

All  the  angles  of  a  triangle  are  equal  to  two  right  angles, 

A  is  an  angle  of  a  triangle, 

Therefore  A  is  equal  to  two  right  angles. 
To  argue  that,  because  some  measure  benefits  the  country 
as  a  whole,  it  must  therefore  benefit  every  section  of  the  coun- 
try, would  be  another  instance  of  this  fallacy.  Again,  we 
may  often  find  examples  of  both  Division  and  Composition 
in  the  practice  so  common  in  debate  of  '  taking  to  pieces  ' 
the  arguments  by  which  any  theory  or  proposed  course  of 
action  is  justified.  A  person  would  be  guilty  of  Division 
if  he  should  argue  that,  because  a  complex  theory  is  not 
completely  proved,  none  of  the  arguments  by  which  it  is 
supported  have  any  value.  It  is,  however,  perhaps  more 
common  to  fall  into  the  fallacy  of  Composition  in  combating 
the  arguments  of  an  opponent.  Some  measure,  for  example, 
is  proposed  to  which  a  person  finds  himself  in  opposition. 


§  47-   Material  Fallacies  177 

It  is  usually  easy  to  analyze  the  different  arguments  which 
have  been  advanced  in  support  of  the  measure,  and  to  show 
that  no  single  one  of  these  taken  by  itself  is  sufficient  to  justify 
the  change.  The  conclusion  may  then  be  drawn  with  a 
fine  show  of  logic  that  all  the  reasons  advanced  have  been 
insufficient.  This,  of  course,  is  to  neglect  the  combined 
effect  of  the  arguments;  it  is  to  assume  that  what  is  true  of 
'  all,'  taken  distributively,  is  also  true  of  '  all,'  when  taken 
in  conjunction.  And  often,  as  in  the  case  of  circumstantial 
evidence,  what  gives  a  chain  of  inference  its  strength  is 
not  the  particular  arguments  or  facts  taken  each  for  itself, 
but  what  is  sometimes  called  the  '  consilience '  of  these 
particulars;  that  is,  the  fact  that  they  form  a  connected 
body  of  proof  all  pointing  to  one  conclusion,  so  that  each  part 
has  a  significance,  taken  in  its  relation  to  the  whole  proof, 
which  by  itself  it  would  not  have. 

But  an  affirmative  form  of  the  fallacy  just  mentioned  is 
also  possible  in  cases  where  it  is  attempted  to  prove  the 
possibility  or  probability  of  a  conclusion  by  pointing  to  even 
the  high  probability,  taken  separately,  of  each  one  of  a  num- 
ber of  conditions  which  must  be  true  together,  in  order  that 
the  conclusion  may  be  true.  The  mere  fact  of  a  large  number 
being  possible  separately  may  even  seem  to  the  careless  to 
make  the  conclusion  more  probable,  when  really,  if  the  condi- 
tions must  be  present  together,  this  becomes  less  probable 
the  more  there  are  of  them.  What  should  be  proved  in  such 
cases  is  of  course  the  probability  of  the  conditions  as  a  body; 
and  this  probability  is  always  less  than  that  of  the  least 
probable  among  them  taken  as  occurring  by  itself.  Suppose, 
for  example,  that  we  were  considering  the  probability  of  a 
report  being  true  which  had  been  handed  down  in  succession 

N 


178  Fallacies  of  Deductive  Reasoning 

by  A,  B,  C,  and  D.  What  we  have  to  consider  is  not  the 
probability  of  any  one  of  these  persons  reporting  correctly 
by  himself,  but  that  of  the  correct  transmission  of  the  report 
through  the  entire  series.  Thus,  it  will  be  found  that  if 
the  probability  of  mistake  by  any  one  of  these  persons  is 
only  1  in  5,  the  probability  of  error  in  the  final  result  will  be 
approximately  3  in  5. 

(4)  It  is  often  difficult  to  distinguish  the  various  forms 
of  the  fallacy  of  Accident  from  Composition  and  Division. 
We  have  seen  that  the  last  two  rest  upon  a  confusion  between 
whole  and  part;  or,  as  we  have  already  expressed  it,  on 
an  equivocation  between  the  distributive  and  collective  use 
of  terms.  The  fallacies  of  accident  are  also  due  to  equivo- 
cation. But,  in  this  case,  the  confusion  is  between  essential 
properties  and  accidents,  between  what  is  true  of  a  thing 
in  its  real  nature,  as  expressed  by  its  logical  definition,  and 
what  is  true  of  it  only  under  some  peculiar  or  accidental 
circumstance;  or,  in  other  words,  a  proper  distinction  is  not 
made  between  the  general  import  of  a  principle  and  its  appli- 
cation to  cases  where  special  modifying  conditions  are  present. 

There  are  two  forms  of  this  argument  which  are  usually 
recognized:  (a)  The  Direct  or  Simple  Fallacy  of  Accident, 
which  consists  in  arguing  that  what  is  true  of  a  thing  generally, 
is  also  true  of  it  under  some  accidental  or  peculiar  circum- 
stance ;  or  that  a  proposition  generally  true  is  true  in  exactly 
the  same  way  when  special  conditions  are  present.  The 
old  logicians  expressed  this  in  the  formula,  a  dicto  simpliciter 
ad  dictum  secundum  quid.  The  second  form  is  (b)  the  Con- 
verse Fallacy  of  Accident,  which  consists  in  arguing  that 
what  is  true  of  a  thing  under  some  condition  or  accident, 
can  be  asserted  of  it  simply  or  in  its  essential  nature;  or 


§  47-    Material  Fallacies  179 

that  a  statement  which  is  true  when  certain  conditions  are 
present  is  true  generally.  The  formula  for  this  is,  a  dicto 
secundum  quid  ad  dictum  simpliciter. 

It  would  be  an  illustration  of  the  direct  fallacy  to  reason 
that,  because  man  is  a  rational  being,  therefore  a  drunken 
man  or  an  angry  man  will  be  guided  by  reason.  Similarly, 
we  should  commit  this  fallacy  if  we  were  to  argue  that  be- 
cause beefsteak  is  wholesome  food,  it  would  be  good  for  a 
person  suffering  with  fever  or  dyspepsia;  or  to  conclude 
from  the  principle  that  it  is  right  to  relieve  the  suffering  of 
others,  that  we  ought  to  give  money  to  beggars. 

It  would  be  a  case  of  the  converse  fallacy  to  argue  that 
because  spirituous  liquors  are  of  value  in  certain  cases  of 
disease,  they  must  therefore  be  beneficial  to  a  person  who 
is  well.  We  should  also  be  guilty  of  the  same  fallacy,  if  we 
should  conclude  that  it  is  right  to  deceive  others,  from  the 
fact  that  it  is  sometimes  necessary  to  keep  the  truth  from  a 
person  who  is  sick,  or  to  deceive  an  enemy  in  time  of  war. 

The  fallacies  of  Accident,  like  all  the  fallacies  of  Equivo- 
cation, are  largely  the  result  of  a  loose  and  careless  use  of 
language.  The  source  of  both  forms  of  the  fallacy  is  one 
and  the  same.  They  arise  fom  the  careless  use  of  principles 
or  propositions  without  due  regard  to  the  circumstances 
which  determine  whether  they  are  properly  to  be  applied, 
unmodified  to  the  case  before  us.  By  qualifying  our  terms 
so  as  to  state  the  exact  circumstances  involved,  they  may 
easily  be  detected  and  avoided. 

(5)  The  Dilemmatic  Fallacy  arises  from  the  equivocal 
and  shifting  point  of  view  present  in  the  premises  of  a  di- 
lemma which  fs  open  to  rebuttal.  It  has  been  fully  discussed 
at  the  end  of  Chapter  XL 


i8o  Fallacies  of  Deductive  Reasoning 

(B)  Fallacies  of  Presumption.  —  The  fallacies  of  this 
group  are  the  result  of  presumption  or  assumption  on  the 
part  of  the  person  making  the  argument.  It  is  possible 
(i)  to  assume  the  point  to  be  proved,  either  in  the  premises 
of  an  argument,  or  in  a  question  (Petitio  Principii,  and 
Complex  Question);  or  (2)  to  assume  without  warrant  that 
a  certain  conclusion  follows  from  premises  which  have  been 
stated  (Non  Sequitur);  or  (3)  that  the  conclusion  obtained 
is  really  what  is  required  in  order  to  settle  the  question  at 
issue  (Irrelevant  Conclusion). 

(a)  Petitio  Principii,  or  '  Begging  the  Question,'  is  a  form 
of  argument  which  assumes  the  conclusion  to  be  proved. 
This  may  be  done  in  either  of  two  ways,  (a)  We  may  pos- 
tulate the  fact  which  we  wish  to  prove,  or  its  equivalent 
under  another  name.  Thus,  for  example,  we  might  argue 
that  an  act  is  morally  wrong  because  it  is  opposed  to  sound 
ethical  principles.  '  The  soul  is  immortal  because  it  is  a 
simple  and  indecomposable  substance,'  may  be  regarded 
as  another  example  of  this  assumption.  A  '  question-begging 
epithet  '  or  cant  phrase  is  often  used  to  bring  in  such  an 
assumption.  Thus,  Mill  remarks,  when  Cicero  discusses 
whether  certain  propensities,  if  kept  within  limits,  might 
be  regarded  as  virtuous,  he  calls  them  cupiditates,  which 
of  itself  implies  that  they  are  vicious.  We  shall  have  occa- 
sion to  mention  this  fallacious  use  of  epithets  more  at  length 
when  we  come  to  discuss  the  fallacies  of  inductive  reasoning. 
But  (6)  the  question  may  be  begged  by  making  a  general 
assumption  covering  the  particular  point  in  dispute. 
Thus,  if  the  advisability  of  legislation  regulating  the  hours  of 
labour  in  a  mine  or  factory  were  under  discussion,  the  ques- 
tion-begging   proposition,    '  all    legislation  which    interferes 


§47-    Material  Fallacies  181 

with  the  right  of  free  contract  is  bad,'  might  be  propounded 
as  a  settlement  of  the  whole  question. 

A  special  form  of  this  fallacy  results  when  each  of  two 
propositions  is  used  in  turn  to  prove  the  truth  of  the  other. 
This  is  known  as  '  reasoning  in  a  circle,'  or  circulus  in  pro- 
bando.  This  method  of  reasoning  is  often  adopted  when 
the  premise,  which  has  been  employed  to  prove  the  first 
conclusion,  is  challenged.  '  I  should  not  do  this  act,  because 
it  is  wrong.'  '  But  how  do  you  know  that  the  act  is  wrong  ?  ' 
'  Why,  because  I  know  that  I  should  not  do  it.' 

It  is  always  necessary,  then,  to  see  that  the  conclusion 
has  not  been  assumed  in  the  premises.  But,  since  the 
conclusion  always  follows  from  the  premises,  we  may  say 
that  in  one  sense  the  conclusion  is  always  thus  assumed. 
It  is,  therefore,  easy  to  charge  an  opponent  unjustly  with 
begging  the  question.  De  Morgan,  in  his  work  on  Falla- 
cies, says:  "There  is  an  opponent  fallacy  to  the  Petitio 
Principii  which,  I  suspect,  is  of  more  frequent  occurrence: 
it  is  the  habit  of  many  to  treat  an  advanced  proposition  as 
a  begging  of  the  question  the  moment  they  see  that,  if  estab- 
lished, it  would  establish  the  question."  All  argument 
must,  of  course,  start  from  premises  to  which  both  parties 
assent.  But  candour  and  fairness  forbid  us  to  charge  an 
opponent  with  Petitio  because  the  results  of  his  premises 
are  unwelcome.  It  was  Charles  Lamb  who  humorously 
remarked  that  he  would  not  grant  that  two  and  two  are 
four  until  he  knew  what  use  was  to  be  made  of  the  admis- 
sion. 

(2)  The  Complex  Question  is  an  interrogative  form  of 
Petitio.  It  is  not  really  a  simple  interrogation,  but  is  founded 
upon    an    assumption.     It    tacitly    assumes,    that    is,    both 


/82  Fallacies  of  Deductive  Reasoning 

that  certain  things  are  true,  and  that  certain  other  things 
are  false;  and  therefore  any  direct  answer  to  it  always  in- 
volves the  admission  as  true  of  more  than  one  statement. 
Any  discussion  or  argument  whatever,  of  course,  always 
proceeds  on  the  basis  of  certain  assumptions;  but  there 
should  be  principles  that  are  accepted  as  true,  at  least  provi- 
sionally, by  all  the  parties  engaged  in  the  discussion,  and 
they  should  be  as  far  as  possible  made  clear  and  definite 
before  discussion  begins.  In  fact,  this  precaution  of  mak- 
ing as  clear  as  possible  to  oneself  what  one  is  taking  for 
granted  is  the  proper  remedy  against  all  the  fallacies  of  pre- 
sumption. Examples  of  this  fallacy  may  be  found  in  popu- 
lar pleasantries,  such  as,  '  Have  you  given  up  your  drinking 
habits?  '  '  Do  the  people  in  your  part  of  the  country  still 
carry  revolvers?  '  Disjunctive  questions,  too,  always  contain 
an  assumption  of  this  kind:  '  Is  this  an  oak  or  a  chestnut? ' 
'  Does  he  live  in  Boston  or  New  York  ?  '  The  '  leading 
questions  '  which  lawyers  frequently  use  in  examining  wit- 
nesses, but  which  are  always  objected  to  by  the  opposing 
counsel,  are  usually  of  this  character.  Further  instances 
may  perhaps  be  found  in  the  demand  for  explanation  of 
facts  which  are  either  false,  or  not  fully  substantiated;  as, 
e.g.,  '  Why  does  a  fish  when  dead  weigh  more  than  when 
alive  ?  '     '  What  is  the  explanation  of  mind-reading  ?  ' 

(3)  The  Irrelevant  Conclusion,  or  Ignoratio  Elenchi,  con- 
sists in  substituting  for  the  conclusion  to  be  proved  some 
other  proposition  more  or  less  nearly  related  to  it.  This 
fallacy  may  be  the  result  of  an  involuntary  confusion  on 
the  part  of  the  person  employing  it,  or  it  may  be  consciously 
adopted  as  a  controversial  stratagem  to  deceive  an  opponent 
or  an  audience.     When  used  in  this  latter  way,  it  is  usually 


§  47-    Material  Fallacies  183 

intended  to  conceal  the  weakness  of  a  position  by  diverting 
attention  from  the  real  point  at  issue.  This  is,  indeed,  a 
favourite  device  of  those  who  have  to  support  a  weak  case. 
A  counsel  for  the  defence  in  a  law-suit  is  said  to  have  handed 
to  the  barrister  presenting  the  case  a  brief  marked,  '  No 
case;  abuse  the  plaintiff's  attorney.'  To  answer  a  charge 
or  accusation  by  declaring  that  the  person  bringing  the  charge 
is  guilty  of  as  bad,  or  even  worse,  things,  —  what  is  some- 
times called  the  tu  quoque  form  of  argument  —  is  also  an 
example  of  this  fallacy. 

Apart  from  such  wilful  perversions  or  confusions,  many 
unintentional  instances  of  this  fallacy  occur.  In  controver- 
sial writing,  it  is  very  natural  to  assume  that  a  proposition 
which  has  some  points  of  connection  with  the  conclusion  to 
be  established,  is  '  essentially  the  same  thing,'  or  '  practically 
the  same,  as  the  thesis  maintained.'  Thus  one  might  take 
the  fact  that  a  great  many  people  are  not  regular  church- 
goers, as  a  proof  of  the  proposition  that  religion  and  morality 
are  dying  out  in  the  country.  Many  of  the  arguments 
brought  against  scientific  and  philosophical  theories  belong  to 
this  class.  Mill  cites  the  arguments  which  have  been  urged 
against  the  Malthusian  doctrine  of  population,  and  Berke- 
ley's theory  of  matter.  We  may  quote  the  passage  refer- 
ring to  the  former:  "Malthus  has  been  supposed  to  be  re- 
futed, if  it  could  be  shown  that  in  some  countries  or  ages 
population  has  been  nearly  stationary,  as  if  he  had  asserted 
that  population  always  increases  in  a  given  ratio,  or  had  not 
expressly  declared  that  it  increases  only  in  so  far  as  it  is  not 
restrained  by  prudence,  or  kept  down  by  disease.  Or,  per- 
haps, a  collection  of  facts  is  produced  to  prove  that  in  some 
one  country  with  a  dense  population  the  people  are  better 


1 84  Fallacies  of  Deductive  Reasoning 

off  than  they  are  in  another  country  with  a  thin  one,  o\ 
that  the  people  have  become  better  off  and  more  numerous 
at  the  same  time;  as  if  the  assertion  were  that  a  dense  popu- 
lation could  not  possibly  be  well  off."  *  Ignorance  of  the 
methods  proper  to  the  subject  under  discussion  is  a  pro- 
lific source  of  such  fallacies  as  this.  Mere  knowledge  of 
facts  without  knowing  their  meaning  is  not  enough,  and 
those  whose  knowledge  is  of  this  description  do  not  see  what 
the  real  questions  at  issue  are,  or  what  constitutes  a  real 
proof  in  different  subject-matters.  As  Whately  puts  it, 
'This  is  to  learn  a  good  many  answers  without  the  ques- 
tions.' The  history  of  modern  attempts  to  '  square  the  circle' 
furnishes  good  examples  of  this;  and  scientists  of  unques- 
tioned authority  in  their  own  field  are  often  led  astray  in 
this  way  when  they  attempt  to  deal,  without  proper  prepa- 
ration, with  questions  belonging  to  another  science,  or  to 
philosophy  or  religion. 

There  are  several  cases  or  forms  of  Irrelevant  Conclusion 
to  which  special  names  have  been  given,  and  which  it  is 
important  to  consider  separately.  When  an  argument 
bears  upon  the  real  point  ?t  issue,  it  is  called  argumentum 
ad  rem.  But,  on  the  other  hand,  there  are  the  following 
special  ways  of  obscuring  the  issue:  argumentum  ad  hom- 
inem,  argumentum  ad  populum,  argumentum  ad  ignorantiam , 
argumentum  ad  verecundiam,  argumentum  ad  misericordiam, 
the  Fallacy  of  Objections,  and,  by  extension,  the  argumentum 
ad  baculum. 

The  argumentum  ad  hominem  is  an  appeal  to  the  char- 
acter, principles,  or  former  profession  of  the  person  against 
whom  it  is  directed.  It  has  reference  to  a  person  or  persons, 
1  Logic,  Bk.  V.,  Ch.  VII.,  §  3. 


§  47-    Material  Fallacies  185 

not  to  the  real  matter  under  discussion.  In  order  to  con- 
fuse an  opponent,  and  discredit  him  with  the  audience,  one 
rnay  show  that  his  character  is  bad,  or  that  the  views  which 
he  is  now  maintaining  are  inconsistent  with  his  former  pro- 
fessions and  practice.  Or,  on  the  defensive  side,  the  char- 
acter of  the  advocate  of  the  point  at  issue  may  be  praised. 
Or  the  argument  may  be  used  with  the  hope  of  persuading 
the  opponent  himself.  We  then  try  to  convince  him  that 
the  position  which  he  maintains  is  inconsistent  with  some 
other  view  which  he  has  previously  professed,  or  with  the 
principles  of  some  sect  or  party  which  he  has  approved. 
Or  we  may  appeal  to  his  interests  by  showing  him  that  the 
action  proposed  will  affect  injuriously  some  cause  in  which 
he  is  concerned,  or  will  benefit  some  rival  sect  or  party. 
In  all  of  these  cases  the  real  point  at  issue  is,  of  course, 
evaded.  The  only  case  in  which  such  an  argument  seems 
at  all  admissible  for  the  logical  purpose  of  establishing  truth, 
and  not  merely  securing  conviction,  is  when  the  known  bad 
character  or  untrustworthiness  of  some  person  is  appealed 
to  in  order  to  impeach  the  evidence  he  may  give.  Here  it 
at  least  assists  us  to  exclude  what  is  false,  and  is  therefore  a 
relevant  argument,  though  one  of  merely  negative  character. 
The  argumentum  ad  populum  is  an  argument  addressed  to 
the  feelings,  passions,  and  prejudices  of  people  rather  than 
an  unbiassed  discussion  addressed  to  the  intellect.  The  use 
of  question-begging  epithets  frequently  accompanies  this 
fallacy.  The  argumentum  ad  misericordiam  seems  to  be  only  a 
special  case  of  this  fallacy,  when  an  appeal  is  made  to  the  pity 
or  sympathy  which  people  may  be  made  to  feel  for  a  person 
accused  of  crime.  Or  sometimes  it  may  be  attempted  to  rec- 
ommend some  party  or  cause  by  arousing  such  feelings  for 


x  86  Fallacies  of  Deductive  Reasoning 

its  adherents,  or  a  law,  by  dwelling  on  the  plight  of  those 
whom  it  would  perhaps  relieve. 

The  argumentum  ad  ignorantiam  is  an  attempt  to  gain  sup- 
port for  some  position  by  dwelling  upon  the  impossibility  of 
proving  the  opposite.  Thus  we  cannot  prove  affirmatively 
that  spirits  do  not  revisit  the  earth,  or  send  messages  to  former 
friends  through  'mediums.'  Now  it  is  not  unusual  to  find 
ignorance  on  this  subject  advanced  as  a  positive  ground  of 
conviction.    The  argument  seems  to  be:  — 

It  is  not  impossible  that  this  is  so, 
What   is   not   impossible   is  possible, 


Therefore  it  is  possible  that  this  is  so. 
The  fallacy  arises  when  we  confuse  what  is  only  abstractly 
possible — i.e.  what  we  cannot  prove  to  be  impossible  —  with 
what  is  really  possible,  i.e.  with  what  we  have  some  positive 
grounds  for  believing  in,  though  these  grounds  are  not  suffi- 
cient to  produce  conviction. 

The  argumentum  ad  verecundiam  is  an  appeal  to  the  rever- 
ence which  most  people  feel  for  a  great  name,  or  for  long- 
established  usages.  This  method  of  reasoning  attempts  to 
settle  a  question  by  referring  to  the  opinion  of  some  acknow- 
ledged authority,  without  any  consideration  of  the  arguments 
which  are  advanced  for  or  against  the  position.  It  is,  of  course, 
right  to  attach  much  importance  to  the  views  of  great  men,  and 
to  the  presumptive  evidence  of  value  given  by  ancient  and 
continued  use ;  but  we  must  not  suppose  that  the  opinions  of 
the  great,  or  the  presumed  validity  of  custom,  amount,  by 
themselves  and  unexamined,  to  final  proof,  or  forbid  us  to 
consider  the  matter  for  ourselves,  if  we  are  competent  to  do  so. 

There  is,  however,  a  more  common,  though  much  less  justi- 


§  47'   Material  Fallacies  187 

iiable,  form  of  the  argument  from  authority.  A  man  who  is 
distinguished  for  his  knowledge  and  attainments  in  some  par- 
ticular field,  is  often  quoted  as  an  authority  upon  questions  with 
which  he  has  no  special  acquaintance.  The  prestige  of  a  great 
name  is  thus  irrelevantly  invoked  when  no  significance  properly 
attaches  to  it.  Thus,  for  example,  a  successful  general  is 
sometimes  supposed  to  speak  with  authority  upon  problems 
of  statecraft,  and  the  opinions  of  prominent  clergymen  are 
quoted  regarding  the  latest  scientific  or  political  theories. 

The  Fallacy  of  Objections  consists,  as  Whately  states  it,  in 
"  showing  that  there  are  objections  against  some  plan,  theory, 
or  system,  and  thence  inferring  that  it  should  be  rejected; 
when  that  which  ought  to  have  been  proved  is,  that  there  are 
more  or  stronger  objections  against  the  receiving  than  the 
non-receiving  of  it."  This  fallacy,  he  remarks,  is  "  the  strong- 
hold of  bigoted  anti-innovators."  In  any  matter  of  dispute, 
there  will  be  objections  to  any  solution  offered;  but  this,  of 
itself,  is  no  disproof  of  the  conclusion  attacked,  provided  we 
have  some  positive  grounds  for  it.  "There  are  objections," 
Dr.  Johnson  once  said,  "against  a  plenum,  and  objections 
against  a  vacuum;  but  one  of  them  must  be  true." 

When  all  these  forms  of  the  fallacy  fail,  there  is  still  one 
recourse  remaining,  which  takes  the  matter  beyond  the  bound- 
aries of  logic;  though,  indeed,  the  other  forms  are  in  their 
way  quite  as  irrelevant.  This  is  the  argumenlum  ad  bacidum, 
which  we  may  translate  in  current  phrase  as  the  'appeal  to 
the  big  stick.' 

(4)  The  fallacy  of  non  sequitur,  or  the  Fallacy  of  the  Conse- 
quent, occurs  when  the  conclusion  does  not  really  follow  from 
the  premises  by  which  it  is  supposed  to  be  supported.  The 
following  example  may  serve  as  an  illustration:  — 


1 88  Fallacies  of  Deductive  Reasoning 

Pennsylvania  contains  rich  coal  and  iron  mines, 
Pennsylvania  has  no  sea-coast, 

Therefore  the  battle  of  Gettysburg  was  fought  in  that  state. 

This  argument,  of  course,  is  thoroughly  inconsequent,  and 
would  deceive  no  one.  But  when  the  conclusion  repeats  some 
words  or  phrases  from  the  premises,  we  are  likely,  when  not 
paying  close  attention,  to  be  imposed  upon  by  the  mere  form 
of  the  argument.  We  notice  the  premises,  and  remark  that 
the  person  using  the  argument  advances  boldly  through  'there- 
fore' to  his  conclusion.  And  if  this  conclusion  appears  to  be 
related  to  the  premises,  and  sounds  reasonable,  the  argument 
is  likely  to  be  accepted.  The  following  example  will  illustrate 
this:  — 

Every  one  desires  happiness,  and  virtuous  people  are  happy, 
Therefore  every  one  desires  to  be  virtuous. 

A  rather  frequent  form  of  this  fallacy  occurs  when  we 
chink,  because  we  have  refuted  an  argument  for  a  theory, 
that  the  theory  itself  is  necessarily  false,  —  which  would 
be  true  only  if  the  refuted  argument  was  the  only  pos- 
sible one  for  the  theory.  Or,  again,  we  may  think  that 
because  a  conclusion  is  true,  a  usual  argument  for  it  is 
also  true;  thus,  for  example,  we  might  think  that  because 
God  exists,  the  general  consent  of  all  mankind,  which  used  to 
be  urged  as  a  proof  of  His  existence,  is  true.  These  forms  of 
the  fallacy  may  be  regarded  as  simply  a  breach,  within  a  con- 
tinued argument,  of  the  rules  of  the  hypothetical  syllogism 
—  'affirm  the  antecedent,  or  deny  the  consequent.'  For 
in  the  first  form,  we  argue  that  because  a  proof  is  false,  the 
conclusion  which  would  certainly  be  true  if  it  were  true,  is 


§  47-    Material  Fallacies  189 

therefore  false  ;  and,  in  the  second,  we  argue  that  because  a 
conclusion  is  true,  therefore  an  argument  on  which  it  is 
usually  made  to  depend  is  also  true. 

What  is  known  as  the  False  Cause  (non  causa  pro  causa; 
post  hoc  ergo  propter  hoc)  is  the  inductive  fallacy  correspond- 
ing to  the  non  sequitur.  In  this  we  assume  that  one  thing 
is  the  cause  of  another  merely  because  we  have  known  them 
to  happen  together  a  number  of  times.  The  causal  relation 
is  assumed  without  any  analysis  or  examination,  on  the 
ground  of  some  chance  coincidence.  Thus  a  change  in  the 
weather  may  be  attributed  to  the  moon,  or  the  prosperity 
of  the  country  to  its  laws  requiring  Sunday  observance. 
Or  in  a  case  where  there  is  really  a  causal  connection  we 
may  take  the  cause  for  the  effect,  or  the  effect  for  the  cause. 
Whately's  example  of  this  is  a  good  one,  because  it  is  a 
popular  fallacy  often  to  be  met  with,  especially  where  the 
action  of  natural  selection  is  not  realized.  It  is  frequently 
assumed,  because  the  animals  and  men  native  to  countries  of 
inclement  climate,  where  the  conditions  of  life  are  severe,  are 
usually  robust,  that  the  hardships  they  are  forced  to  undergo 
in  youth  are  the  cause  of  this  hardiness ;  whereas,  as  a 
matter  of  fact,  their  hardiness  was  the  cause  of  their  having 
survived  the  hardships.  Popular  notions  of  hygiene  are 
sometimes  largely  dependent  on  this  confusion.     (Cf.  §  73.) 

REFERENCES 

J.  S.  Mill,  Logic,  Bk.  V. 

A.  Sidgwick,  Fallacies  [Int.  Scient.  Series]. 

R.  Whately,  Elements  of  Logic,  Bk.  III. 


PART   II.  — INDUCTIVE    METHODS 

CHAPTER    XIII 

THE   PROBLEM   OF   INDUCTION 

§48.  The  Problem  of  Induction. —  In  Part  I.  we  have 
studied  the  general  nature  of  the  syllogism,  and  have  learned 
what  conditions  must  be  fulfilled  in  order  to  derive  valid 
conclusions  from  given  premises.  But  the  question  how  the 
premises  themselves  are  established  was  not  discussed.  It  is 
true  that  the  premises  of  one  syllogism  are  sometimes  proved 
by  means  of  a  Prosyllogism,  and  that  it  maybe  possible  to  find 
in  turn  general  propositions  to  support  the  premises  of  this 
latter  argument.  But  somewhere  this  process  of  formal  proof 
must  have  an  end.  At  last  we  reach  propositions  concerning 
which  we  can  say  only  that  their  truth  is  guaranteed  by  experi- 
ence. It  is  from  experience  that  propositions  are  obtained 
like, '  man  is  by  nature  a  social  being,'  c  water  is  composed  of 
hydrogen  and  oxygen,'  which  serve  as  the  premises  of  syllo- 
gisms. To  say  that  these  propositions  are  learned  through  ex- 
perience, does  not  however  mean  that  they  have  been  obtained 
without  thinking.  For  to  experience  is  not  merely  to  feel  or 
to  have  sensations;  it  is  also  to  put  things  together,  to  interpret, 
to  appreciate  to  some  extent  what  our  sensations  stand  for 
and  signify.  When  I  say,  'yonder  tree  is  an  elm,'  this  proposi- 
tion is  the  outcome  of  my  own  thinking;  it  is  my  interpretation, 

190 


§  48.    The  Problem  of  Induction  191 

on  the  basis  of  past  experience,  of  certain  sensations  of  colour 
and  light  and  shade,  together,  it  may  be,  with  certain  muscular 
sensations  from  the  movements  of  the  eyes.  Our  thought  is 
constantly  bringing  new  sensations  and  perceptions  into 
relation  with  former  experiences,  and  in  this  way  building 
up  and  organizing  our  world  of  knowledge.  To  interpret 
the  real  world  —  not  only  the  physical  world,  but  the  psycho- 
logical  and  the  social  world  as  well  —  is  then  the  business 
of  thought,  and  this,  as  we  have  seen,  is  to  relate  the  new  in 
some  way  to  what  we  already  understand.  Our  sense  percep- 
tions, just  as  they  come,  are  without  order  or  system. 
Think,  for  example,  of  the  various  things  you  are  sensing  at 
the  present  time.  The  greater  part  of  these  are  not  consciously 
attended  to  or  thought  about;  they  are  taken  for  granted  or 
roughly  classified  on  the  basis  of  some  past  experience.  But 
if  one  is  really  thinking,  there  is  some  fact  or  relation  that  is 
taken  as  a  problem,  and  for  which  one  is  seeking  an  interpreta- 
tion, i.e.  some  way  of  thinking  this  fact  or  relation  that  will 
bring  it  into  place  and  adjust  it  to  what  is  already  known. 

Apart  from  this  task  of  interpreting  the  real  world,  thought 
has  no  function,  and  does  not  exist.  Syllogistic  reasoning  is 
not  a  distinct  and  separate  kind  of  thinking,  but  is  a  necessary 
part  of  the  work  of  building  up  our  knowledge  of  the  world  in 
systematic  form.  Without  thinking,  then,  no  knowledge,  no 
real  experience.  But  we  must  remember  that  thinking  is  no 
mere  play  of  ideas  in  our  heads.  It  exists  only  in  relation  to 
what  is  objective  and  real.  In  a  certain  sense  it  always  goes 
back  to  a  datum,  to  perception.  Kant's  famous  saying  that 
'perceptions  without  conceptions  (i.e.  thoughts)  are  blind, 
while  conceptions  without  perceptions  are  empty,'  is  well 
worth  remembering. 


192  The  Problem  of  Induction 

The  problem  of  Induction,  with  which  we  are  primarily  con- 
cerned in  this  part  of  the  book,  is  how  we  are  able  to  derive 
from  experience  general  propositions  or  principles.  It  is  on 
these,  as  we  have  seen,  that  we  base  our  conclusions  in 
syllogistic  reasoning.  The  difficulty  is  that  experience 
seems  to  give  information  regarding  individual  things  and 
their  qualities  only.  One  learns  by  experience  the  qualities 
of  this  rose,  or  of  this  piece  of  iron;  but  how  is  one  to  dis- 
cover the  general  nature  of  the  rose  or  of  iron  as  such  ?  As 
a  matter  of  fact,  we  are  constantly  deriving  general  statements 
from  individual  experiences;  and  in  doing  this  we  usually 
bring  up,  in  a  more  or  less  systematic  way,  a  number  of  cases 
or  instances  and  use  them  as  the  basis  of  the  general  statement. 
And  this  process  of  generalization,  or  passing  to  a  general 
conclusion  on  the  ground  of  certain  instances  or  cases  that 
have  been  advanced,  may  be  called  Induction  (e7raycoy^). 
This  definition  is,  of  course,  only  preliminary,  and  does  not 
attempt  to  distinguish  valid  and  invalid  induction.  We  have 
to  go  on  to  consider  more  in  detail  both  the  conditions  neces- 
sary to  render  the  process  valid,  and  the  meaning  of  the  gen- 
eralization at  which  we  arrive. 

§  49.  The  Enumeration  of  Instances.  —  In  the  first  place, 
Induction  is  not  the  outcome  of  a  complete  enumeration  of 
instances;  but  from  an  examination  of  a  certain  number  we 
infer  the  general  mark  or  principle  that  is  involved  in  all  the 
instances.  Where  all  the  instances  have  been  examined,  the 
result  may  be  summed  up  at  the  end  in  a  proposition  that  is 
universal  in  form;  but  in  such  a  case  there  has  been  no  Induc- 
tion, no  passage  to  any  truth  that  is  really  general.  For  ex- 
ample, after  measuring  each  individual  in  a  company  and 
Ending  that  A  is  less  than  six  feet  in  height,  B  less  than  six 


§  49-    The  Enumeration  of  Instances  193 

feet,  and  so  on  for  the  rest,  I  might  make  the  assertion,  '  No 
one  in  this  company  is  more  than  six  feet  tall.'  This,  however, 
would  be  nothing  more  than  a  summation  of  results,  and  not  a 
genuine  Induction  at  all.  Nevertheless,  some  writers  re- 
gard such  procedure,  where  all  the  instances  are  examined,  as 
the  only  perfect  form  of  induction.  Thus  Jevons  says:  "An 
Induction,  ...  is  called  Perfect,  when  all  of  the  possible 
cases  or  instances  to  which  the  conclusion  can  refer  have  been 
examined  and  enumerated  in  the  premises."1  On  the  other 
hand,  where  it  is  impossible  to  examine  all  the  cases,  the  induc- 
tive process  is  regarded  as  Imperfect  by  the  same  writer,  and 
the  conclusion  expressed  in  the  general  law  as  only  probable. 
Now  this  view,  though  mistaken,  is  interesting  because  it 
assumes  that  it  is  the  business  of  Induction  to  count  instances. 
When  it  is  possible  to  examine  all  the  cases  we  can  have  cer- 
tainty ;  when  this  is  impossible  (as  is  usually  true),  the  unexam- 
ined instances  have  to  be  regarded  as  more  or  less  probable  only. 
No  other  conclusion  is  possible  so  long  as  we  merely  enumerate 
or  cite  instances  without  attempting  to  analyze  them.  A 
mere  factual  connection  of  two  events,  P  and  Q,  though  ex- 
perienced a  thousand  times,  does  not  warrant  the  universal 
proposition,  'All  P  is  Q.'  As  a  matter  of  fact,  scientific  In- 
duction always  does  get  beyond  a  mere  citation  of  unanalyzed 
instances.  "  Induction  which  proceeds  by  merely  citing  in- 
stances," says  Bacon,  "  is  a  childish  affair,  and  being  without 
any  certain  principle  of  inference  it  may  be  overthrown  by  a 
contradictory  instance.  Moreover,  it  usually  draws  the 
conclusion  from  too  small  a  number  of  instances,  taking  ac- 
count only  of  those  that  are  obvious."  2    This  is  an  excellent 

1  Elementary  Lessons  in  Logic,  pp.  212-213. 

2  Novum  Qygonum,  Bk.  I.,  Aph.  CV.     "Inductio  enim  quae  procedit 


194  The  Problem  of  Induction 

description  of  the  popular  unscientific  way  of  seeking  to  estab 
lish  universal  connections  between  events,  by  citing  random 
instances  where  the  events  have  happened  to  be  found  together. 
It  is  generally  easy,  for  example,  to  cite  instances  where  dreams 
have  come  true,  or  where  one  member  of  a  dinner  party  of 
thirteen  has  died  within  a  year.  This  species  of  Induction  is, 
as  Bacon  says,  "res  puerilis"  since  it  simply  asserts  the  con- 
nection without  justifying  it  or  making  it  intelligible,  by  bring- 
ing to  light  any  principle  of  coherency.  The  possibility  of 
contradictory  instances  is  not  excluded,  and  the  cases  cited 
lack  definiteness  and  precision,  no  account  being  taken  of  the 
attendant  circumstances  and  conditions. 

It  should  be  clear,  on  reflection,  that  scientific  Induction 
aims  at  establishing  a  universal  law  that  does  not  refer  pri- 
marily to  cases  or  instances  at  all.  And  the  method  which  it  em- 
ploys, as  will  be  shown  later,  is  to  discover  the  law  by  analyzing 
the  instances  and  reading  it  out  of  them,  rather  than  by  merely 
summing  them  up.  When  I  conclude  inductively  that  'senti- 
mental people  are  selfish,'  or  that '  the  maple  has  a  forked  fruit- 
key,'  the  universal  statement  is  not  to  be  taken  as  merely 
summing  up  instances.  Such  propositions  are  rather  asser- 
tions about  universal  types  or  kinds  — the  nature  of  senti- 
mental people  as  such,  or  of  maple  trees  as  such.  What  has 
been  established,  granting  that  the  induction  is  valid,  is  a 
coherence  of  characters  forming  a  kind  or  type,  so  that  the 
conclusions  might  be  expressed  in  hypothetical  form:  'if 
sentimental,  then  selfish,'  '  if  a  maple,  then  a  forked  fruit- 
key.' 

per  enumerationem  simplicem,  res  puerilis  est,  et  precario  concludit,  et 
periculo  exponitur  ab  instan.tia  contradictoria,  et  plerumque  secundum 
pauciora  quam  par  est,  et  ex  his  tantummodo  quae  praesto  sunt,  pronunciat." 


§  49-    The  Enumeration  of  Instances  195 

To  discover  such  universal  principles  of  connection 
through  the  analysis  and  comparison  of  instances  is  the  goal 
of  what  may  be  called  Scientific  Induction.  But  we  may 
also  speak  of  Enumerative  Induction  as  a  lower  and  less 
complete  form.  In  practical  life  we  often  depend  with 
confidence  on  a  conclusion  which  is  based  on  a  somewhat 
careful  survey  of  instances.  It  is,  of  course,  easier  to  rest 
on  the  authority  of  the  instances,  taking  the  connection  as  a 
fact,  than  to  set  systematically  to  work  to  analyze  the  in- 
stances in  a  scientific  way  in  order  to  determine  exactly  the 
universal  form  of  the  law.  It  is  likewise  clear  that  these 
unanalyzed  or  only  partially  analyzed  instances  form  the 
starting-point  for  scientific  induction;  and  that,  therefore, 
Enumeration  must  often  play  an  important  part  in  the  pre- 
liminary stages  of  an  investigation.  But  in  certain  fields 
of  investigation  we  have  to  go  on  counting  instances  because 
there  seems  to  be  nothing  else  to  do.  We  simply  find  P 
and  Q  invariably  conjoined  as  a  fact  in  experience,  but  are 
unable  to  analyze  out  the  conditions  and  so  either  mediate 
the  connection,  or  exhibit  the  precise  form  of  the  law.  We 
cannot  get  a  genuinely  universal  proposition  asserting,  'P 
as  such  is  connected  with  Q  as  such,'  or,  '  if  P,  then  Q.' 
But  the  Enumerative  conclusion  simply  affirms  that  all 
instances  of  P  (so  far  as  experienced)  are  connected  with 
Q.  Nor  is  the  particular  nature  of  the  connection  defined 
in  this  form  of  Induction.  P  and  Q,  for  example,  may  be 
connected  directly,  or  in  some  indirect  way,  as  through  a 
common  dependence  on  some  third  thing,  M.  In  the  next 
chapter  something  further  will  be  said  of  Enumeration,  and 
how  it  may  contribute,  when  used  intelligently,  to  the  ends 
of  scientific  Induction.     Considered  in   itself,  however,  as 


196  The  Problem  of  Induction 

dealing  merely  with  instances,  we  see  how  far  it  falls  short, 
both  in  certainty  and  exactness,  of  the  ideals  of  scientific 
knowledge. 

§  50.  Induction  through  Analysis.  —  Scientific  Induction, 
then,  aims  at  discovering  some  typical  character  or  law  of 
behaviour.  This  usually  requires  the  examination  of  a 
considerable  number  of  instances.  But  the  general  propo- 
sition is  not,  however,  obtained  by  simply  counting  the 
instances,  or  by  adding  them  together.  The  purpose  of 
taking  a  number  of  instances  is  to  facilitate  analysis,  to  aid 
us  in  eliminating  characters  or  circumstances  which  are 
accidental  or  irrelevant,  and  at  the  same  time,  through  these 
exclusions,  to  exhibit  and  define  more  clearly  the  essential 
character  and  relations  of  the  subject  we  are  investigating. 
The  process  of  analysis  is  thus  at  the  same  time  a  process 
of  synthesis;  the  process  of  excluding  the  irrelevant,  a 
process  of  defining  the  essential.  But  it  should  be  noted 
that  if  the  instances  are  to  lead  to  this  result  they  must,  so 
to  speak,  be  selected  for  this  purpose.  They  are  not  likely 
to  be  instructive,  if  they  are  chosen  at  haphazard.  If  the 
instances  were  all  alike,  for  example,  we  should  not  gain  any- 
thing by  adding  to  their  number,  or  if  we  could  discover 
nothing  in  common  among  them,  we  should  not  be  likely  to 
select  them.  It  is  clear,  then,  that  instances,  to  be  instructive, 
must  be  selected  with  reference  to  the  purpose  of  the  inves- 
tigation, and  that  the  work  of  selecting  instances  is  an  essen- 
tial part  of  the  work  of  induction.  It  is  with  this  end  in  view 
that  we  extend  our  observations  over  as  wide  an  area  as 
possible,  drawing  instances  from  different  parts  of  the  field. 
In  natural  history,  for  example,  specimens  are  taken  from  dif- 
ferent localities,  in  order  to  determine  by  comparison  what. 


§  5°-    Induction  through  Analysis  197 

features  are  specific  or  generic  characters,  and  what  mere 
'  local  variations.'  What  we  seek  to  obtain  is  not  merely  a 
number  of  instances,  but  instances  which  show  differences 
that  might  be  significant  for  our  problem.  What  differences 
or  circumstances  might  be  significant,  we  cannot,  of  course, 
know  in  advance.  We  can  only  guess,  guided  by  our  past 
experience,  what  might  make  a  difference,  and  hope,  by  draw- 
ing instances  from  different  parts  of  the  field,  to  include  all 
the  significant  circumstances.  The  function  which  the 
instances  when  thus  selected  fulfil  is,  of  course,  to  exhibit 
what  is  essential  by  eliminating  circumstances  which  are, 
for  the  purposes  of  the  investigation,  superfluous  and  irrele- 
vant. 

Experimentation,  when  it  is  possible,  is  another  way  of 
performing  the  same  work  of  analysis  and  elimination. 
Hence  in  fields  where  experiments  can  readily  be  made, 
Induction  does  not  have  to  depend  upon  an  assemblage  of 
instances.  The  experimenter,  having  control  of  the  con- 
ditions, can  produce  the  variations  he  wishes  to  observe, 
changing  one  thing  at  a  time  and  noting  the  result.  In  this 
way,  he  is  able  to  strip  the  phenomenon  of  superficial  fea- 
tures that  are  connected  with  it  only  accidentally,  or  in  a  par- 
ticular case,  and  by  so  doing  lay  bare  its  universal  properties 
and  modes  of  acting.  But  in  experimenting,  just  as  in  col- 
lecting instances,  there  must  be  a  guiding  idea  or  purpose. 
In  both  cases  alike,  information  is  gained  only  by  having 
questions  or  provisional  guesses  in  mind,  and  then  selecting 
for  observation  what  is  necessary  to  enable  us  to  decide 
which  guesses  are  false  and  which  true. 

What  guides  the  selection  of  instances  in  an  inductive 
inquiry,  and  also  determines  the  character  of  the  experiments 


198  The  Problem  of  Induction 

^o  be  performed,  is  the  tentative  conception  or  hypothesis 
which  the  investigator  has  in  mind.  We  must  look,  both 
in  collecting  instances  and  in  setting  up  experiments,  for 
facts  which  are  significant,  that  is,  which  will  help  to  answer 
the  questions  we  have  in  mind.  Bacon  discusses  at  length, 
and  classifies  under  twrenty-seven  different  heads,  what  he 
calls  Prerogative  Instances,  which,  as  especially  instructive, 
should  be  the  first  and  last  objects  of  our  investigation. 
Some  of  his  headings  are:  '  Solitary  instances,'  '  migrating 
instances '  (where  the  phenomenon  is  in  process  of  coming 
into  existence  or  disappearing),  '  clandestine  instances,' 
'deviating  instances'  (as  sports,  or  pathological  cases), 
'  bordering  instances,'  and  '  crucial  instances.'  This  last 
name  {instantia  cruris)  is  drawn  from  the  metaphor  of 
the  cross  erected  where  two  roads  meet  to  indicate  the 
different  directions.  When  we  have  alternative  conceptions 
or  explanations  in  mind,  either  of  which  appears  possible, 
we  look  for  some  crucial  instance,  or  devise  some  crucial 
experiment  that  will  point  the  way  by  eliminating  one  of  the 
alternatives.1  To  know  what  facts  would  really  be  crucial 
in  any  given  case,  it  is,  of  course,  necessary  to  have  some 
definite  and  systematic  knowledge  of  the  field  in  which  the 
phenomenon  under  investigation  falls.  Only  when  this 
condition  is  realized,  are  we  able  to  interpret  rightly  the 
bearing  of  the  new  instance  or  experiment  on  our  problem. 
The  process  of  Induction,  then,  might  be  represented  in 
the  form  of  a  Disjunctive  Syllogism,  where  the  conclusion 
is  reached  by  eliminating  successively  all  but  one  of  the 
Disjunctive  members.     For  example:  — 

1  Examples  of  crucial  experiments  may  be  found  among  the  miscellaneous 
rxercises  at  the  end  of  this  volume. 


§  50.    Induction  through  Analysis  199 

This  phenomenon,  P,  is  either  A,  or  B,  or  C. 

These  facts  prove  that  it  is  not  A;  and  these  that  it  is  not  B. 
Therefore  P  must  be  C 

This  account  is  fundamentally  correct  in  principle,  though 
the  Disjunctive  Syllogism  represents  the  process  as  more 
formal  than  it  really  is.  It  is  not  to  be  supposed  that  at 
the  beginning  of  an  inductive  investigation  all  the  possibil- 
ities are  definitely  and  disjunctively  formulated.  The  va- 
rious possibilities,  and  their  relation  to  one  another,  rather 
come  to  light  as  the  examination  and  analysis  proceed. 
And,  at  the  end,  the  conclusion  is  never  merely  the  result 
of  the  process  of  exclusion.  In  other  words,  we  do  not  accept 
C  merely  because  we  cannot  think  of  anything  else;  but, 
through  the  process  of  excluding  A  and  B,  C  has  become, 
to  some  extent  at  least,  positively  denned  and  determined. 
In  dealing  with  any  real  problem,  we  cannot  make  any 
significant  denial  without  thereby  implicitly  affirming  and 
defining  something  else.  These  considerations  will  come 
up  for  discussion  again,  particularly  in  Chapter  XVIII., 
where  an  account  is  given  of  the  more  explicit  use  and  nature 
of  hypotheses.  In  the  meantime,  however,  the  disjunctive 
principle  may  be  regarded  as  the  working  basis  of  inductive 
procedure,  though,  especially  in  the  earlier  stages  of  this 
process,  the  disjunctive  members  are  not  formally  enumer- 
ated, or  set  over  against  one  another  as  exclusive  possibilities. 

Where  now,  we  may  ask,  do  the  conceptions  which  are 
thus  put  forward  in  more  or  less  definitely  disjunctive  form, 
and  tested  by  means  of  instances  and  experiments,  have 
their  source?  They  arise  in  the  mind  itself,  and  are  expres- 
sions of  its  own  theorizing  activity.  These  conceptions, 
however,  are  not  mere  uninstructed  guesses,    but    are    for 


200  The  Problem  of  Induction 

mulated  in  the  light  of  the  knowledge  already  achieved.  In- 
duction, as  a  scientific  process,  bases  itself  on  the  relations 
and  distinctions  that  are  found  in  ordinary  experience,  and 
simply  carries  these  farther  and  makes  them  more  definite 
and  consistent.  Now,  in  the  language  of  ordinary  life,  there 
is  already  given  a  preliminary  classification  and  arrangement 
of  the  fundamental  aspects  of  experience.  In  ordinary 
speech  and  in  everyday  practical  relations,  there  is  present 
a  certain  organization  of  experience.  And  it  is  this  which 
is  taken  as  the  starting-point  for  the  scientific  interpreta- 
tions which  are  to  correct  and  extend  the  old.  The  phe- 
nomenon that  we  set  out  to  interpret  can  only  be  under- 
stood in  the  light  and  with  the  help  of  what  is  already 
assumed  as  known.  It  is  because  we  are  able  to  perceive 
or  imagine  the  likeness  of  the  new  to  something  with  which 
we  are  already  familiar  that  it  is  possible  to  think  it  in 
relation  to  the  rest  of  our  experience.  If  any  phenomenon 
were  to  appear  as  absolutely  unclassifiable,  or  totally  un- 
like anything  ever  experienced  before,  there  would  be  no 
means  of  getting  hold  of  it,  so  to  speak.  And  just  because 
it  might  be  anything,  it  would  be  for  us  as  good  as  nothing. 
Even  to  attend  to  it  wTould  be  impossible,  for  attention  in- 
volves comparison.  But  the  truth  is  that  new  facts  and 
experiences  always  appear  as  modifications  or  variations  of 
existing  experience.  In  other  words,  although  they  have  the 
element  of  unfamiliarity,  it  is  yet  always  possible  to  discover 
in  them  some  point  of  resemblance  or  identity  with  what 
has  gone  before.  This  resemblance  or  analogy  in  certain 
respects  with  what  is  already  familiar  leads  us  to  assume  that 
they  may  be  of  the  same  general  type  or  kind  as  the  latter, 
and  that  they  will  be  found  to  have  similar  properties  oi 


§  50.    Induction  through  Analysis  201 

modes  of  operation.  But  this  is  as  yet  only  an  assumption 
that  must  be  tested  before  being  accepted  as  true.  Further 
analysis  may  show  that  this  assumption  is  based  on  a  mere 
surface  resemblance  which  does  not  warrant  the  interpre- 
tation made.  Or,  as  is  more  usually  the  case,  examination 
may  disclose  analogies  which  only  allow  the  phenomenon  to 
be  classified  as  belonging  to  this  or  that  general  field.  But 
the  point  to  be  noted  is  that  through  analogy  its  sphere  has 
been  determined.  There  are  now  only  a  definite  number 
of  possible  interpretations,  which  take  more  or  less  definitely 
the  form  of  a  disjunctive  proposition;  P  falls  in  the  general 
field  M,  and  is,  therefore,  A  or  B  or  C.  Each  member  is  put 
forward  on  some  positive  ground,  and  is  thus  a  genuine 
possibility,  not  a  mere  unsupported  guess.  But  it  is  only  a 
possibility  —  something  whose  truth  is  still  to  be  deter- 
mined —  and  so  its  function  is  to  operate  as  a  plan  or  schema, 
pointing  the  way  to  further  examination  and  testing  through 
new  instances  and  observations. 

Our  discussion  has  accordingly  shown  that  Induction 
is  able  to  pass  from  instances  to  a  general  conclusion  only 
when  the  instances  are  selected  because  of  their  bearing 
on  conceptions  and  hypotheses  with  which  we  are  experi- 
menting. Moreover,  in  forming  these  tentative  hypotheses, 
we  are  guided  in  the  first  place  by  the  analogy  of  the  phenome- 
non under  investigation  to  what  is  already  known.  Analogy 
and  Hypotheses  are  then  indispensable  in  Induction  from 
the  beginning,  though  the  account  of  the  more  formal  and 
explicit  use  of  these  operations  is  postponed  to  the  latex 
chapters. 


CHAPTER    XIV 

THE    ASSUMPTIONS   OF   INDUCTION  —  STAGES    IN   THE    INDUC- 
TIVE   PROCEDURE 

§  51.  The  Assumptions  of  Induction.  — It  is  part  of  the 
task  of  Logic  to  make  us  conscious  of  the  assumptions  of 
our  thinking.  We  have  found,  in  dealing  with  syllogisms, 
that  it  is  often  necessary  to  look  for  the  premise  or  principle 
assumed  in  drawing  the  conclusion.  But,  in  addition  to 
these  special  assumptions  which  are  taken  as  the  basis  of 
argument  in  particular  cases,  there  are  more  general  assump- 
tions made  by  each  science  in  the  very  process  of  defining 
its  own  standpoint  and  working  conceptions  (cf.  §  95). 
Moreover,  still  more  general  assumptions  may  characterize 
groups  of  sciences,  as,  for  example,  the  natural  sciences, 
the  historical  sciences,  etc.  Finally,  the  question  may  be 
raised  as  to  what  is  assumed  in  all  thinking  —  what  are  the 
universal  assumptions  of  thought — and  what  form  these 
assumptions  take  in  Induction.  In  §  9  we  spoke  of  the 
Laws  of  Thought,  and  under  the  name  of  Identity  and  Con- 
tradiction, reference  was  made  to  the  principles  of  consistency 
on  which  syllogistic  logic  is  based.  Now  since  Induction 
and  Syllogism,  as  both  processes  of  reasoning,  are  different 
rather  in  form  than  in  fundamental  character,  their  assump- 
tions are  not  unrelated  to  each  other.  Indeed,  the  assump- 
tions of  Inductive  thinking  are  more  concrete  expressions 
of  the  laws  of  thought  than  are  the  formal  expressions  of 


§  51.    The  Assumptions  of  Induction  203 

Identity  and  Contradiction,   mentioned  in  connection  with 
the  syllogism. 

What  we  appear  to  assume  in  inductive  reasoning  is  that 
the  reality  with  which  thinking  is  dealing  is  systematic  and 
coherent.  There  is  no  direct  method  of  proving  that  the 
world  is  not  composed  of  a  collection  of  particular  things 
resembling  one  another  more  or  less  in  an  accidental  or  exter- 
nal way,  but  at  bottom  having  nothing  to  do  with  one  another. 
The  only  proof  is  that  it  would  be  impossible  either  to  under- 
stand or  to  deal  practically  with  such  a  world.  For  it  would 
be  a  world  in  which  experience  could  teach  us  nothing,  since 
events  might  happen  in  any  order  or  in  any  way,  and  it 
would  never  be  possible  to  infer  anything.  We  assume,  there- 
fore, and  must  assume,  that  the  world  is  a  cosmos,  not  a  chaos. 
And  this  means  that  there  are  universal  relations  and  con- 
nections of  events  which,  if  once  discovered  in  their  true 
nature,  may  always  be  depended  upon.  '  What  is  once  true 
is  always  true.'  A  (e.g.  the  properties  of  iron,  or  the  prin- 
ciples of  heredity),  once  accurately  determined  and  defined, 
is  A,  however  various  may  be  the  instances  in  which  it  ap- 
pears. To  say,  as  is  sometimes  done,  that  in  Induction 
it  is  assumed  that  what  is  true  of  certain  instances  will  be 
true  of  all  other  instances  which  resemble  these,  is  not  en- 
tirely accurate.  For,  as  we  have  seen,  genuine  induction 
is  not  based  on  instances  at  all,  but  on  the  discovery  through 
analysis  of  a  typical  nature  or  law  of  action.  What  our 
thinking  assumes  is  that  identity  of  law  and  identity  of  nature 
exist  in  and  through  the  diversity  of  things,  and  that  it  is  in 
virtue  of  these  universal  principles  of  connection  that  the  world 
is  a  coherent  and  intelligible  system.  Induction  is  only 
possible  on  the  assumption  that  things  not  only  are  together 


204  ^ie  Assumptions  of  Induction 

but  belong  together.  On  this  assumption  it  has  to  work 
out  the  special  mode  of  'belonging'  in  various  fields  of  phe- 
nomena; to  bring  to  light  the  identity  of  nature  or  law 
that  connects  things  which  at  first  sight  appear  diverse  and 
unrelated. 

(i)  The  question  of  how  this  identity  of  nature,  which  connects 
things,  is  to  be  conceived,  is  a  very  fundamental  one,  both  in  science 
and  philosophy.  We  have  already  seen  that,  to  discover  a  genuine 
identity,  it  is  necessary  to  penetrate  beyond  striking  resemblances 
and  superficial  sense  qualities  to  some  deeper-lying  nature.  More- 
over, the  universal  nature  of  a  thing  cannot  be  discovered  in  the 
form  of  some  essence  or  substance  that  remains  permanent  and 
unchanging.  It  must  rather  be  conceived  dynamically,  as  a  mode 
of  activity,  or  rather  as  a  system  of  activities  in  which  all  the  parts 
are  involved,  and  through  which  they  are  correlated.  And,  fur- 
thermore, the  activity  of  a  thing,  which  constitutes  its  nature, 
carries  it,  so  to  speak,  beyond  its  own  boundaries.  It  acts 
upon  other  things,  and  is  in  turn  influenced  by  them.  Its  so- 
called  properties  are  statements  of  its  relation  to  other  things. 
It  cannot,  therefore,  be  conceived  as  an  isolated,  unchanging 
essence,  but  must  be  defined  through  the  constancy  of  behaviour 
shown  in  its  changing  relations  to  its  environments.  For  exam- 
ple, the  universal  nature  of  man  is  not  found  in  some  unchanging 
substance,  either  material  or  spiritual,  that  inheres  in  the  different 
human  individuals.  It  consists  rather  in  the  system  of  functions, 
physical  and  mental,  through  which  he  expresses  his  relation  to 
the  world  of  persons  and  things.  Nor,  in  the  case  of  man,  are 
the  activities  which  constitute  his  nature  modes  of  reacting  with 
unvaried  uniformity,  but  functions  of  adjustment  and  organiza- 
tion which  develop  in  the  light  of  the  work  they  are  called  upon 
to  perform. 

(2)    The  particular  forms  of  relation  which  are  employed  by 


§  52.    Stages  in  the  Inductive  Process  205 

our  thought  to  connect  things  are  known  as  Categories.  Thus  in 
the  last  paragraph,  we  have  been  insisting  that  things  are  to  be  inter- 
preted by  means  of  dynamical  rather  than  static  categories.  Simi- 
larly we  might  speak  of  Cause  and  Effect,  or  Energy,  or  Unity  of 
Plan  (Purposiveness) ,  as  Categories,  since  they  are  different  forms 
or  conceptions  which  we  employ  in  thinking  things  in  relation. 
Now  each  group  of  sciences  has  its  own  standpoint  and  categories, 
its  own  special  terms  in  which  it  describes  things  and  their  relations. 
Thus  physics  represents  the  phenomena  with  which  it  deals,  as 
mechanically  or  externally  determining  one  another  as  causes  and 
effects,  while  biology  explains  the  actions  of  living  organisms 
largely  in  terms  of  adjustment  and  purpose.  What  particular 
categories  are  employed  by  any  science  depends  partly  on  the 
nature  of  the  facts,  and  partly  on  the  purpose  which  the  science 
has  in  view. 

(3)  If  the  '  law  of  thought'  or 'inductive  assumption'  be  true, 
all  the  various  parts  of  the  world  must  ultimately  be  related 
through  some  law,  or  system  of  laws.  So  much  seems  to  be  implied 
in  the  very  conception  of  a  'universe.'  To  find  some  terms  in 
which  a  universe  can  be  thought  is  the  task  of  philosophy.  What, 
then,  is  to  be  the  highest  or  ultimate  category  of  philosophy?  To 
what  common  conception  may  all  the  diverse  and  seemingly 
irreconcilable  phases  of  the  world  be  reduced  ?  The  two  oppos- 
ing forms  of  answer  given  by  philosophy  to  these  questions  are: 
(1)  the  common  basis  of  all  things  consists  in  some  form  of  matter 
or  physical  energy  (Materialism) ;  (2)  the  unity  of  the  world  is  to 
be  conceived  in  terms  of  an  idea,  or  inner  purposiveness,  through 
which  all  the  parts  and  functions  find  their  explanation  (Idealism). 

§  52.  Stages  in  the  Inductive  Process.  —  Induction  we 
have  already  seen  to  be  a  process  of  interpreting  facts  in 
terms  of  general  conceptions  or  principles.  This  description 
would,  however,  apply  equally  well  to  Deduction;   and,  as  a 


206  The  Assumptions  of  Induction 

matter  of  fact,  these  are  not  different  kinds  of  thinking,  biu 
different  methods,  which  are  necessary  to  supplement  each 
other  in  the  task  of  making  things  intelligible.  The  various 
sciences  have  to  start  with  particular  facts  learned  through 
experience.  The  knowledge  of  general  laws  and  principles 
comes  later,  and  is  derived  from  a  study  of  the  particular  facts. 
It  is  clear,  then,  that  the  procedure  of  all  the  sciences  must  be 
inductive,  at  least  in  the  beginning.  The  various  sciences  are 
occupied,  each  in  its  particular  field,  in  the  task  of  discovering 
order  and  relation  among  phenomena  that  at  first  sight  appear 
to  be  lawless  and  disconnected.  But  in  carrying  out  this 
undertaking  our  thinking  uses  every  means  which  will  help  it 
toward  its  desired  end.  It  is  often  able,  after  pushing  induc- 
tive inquiries  a  little  way,  to  discover  some  general  principle, 
or  to  guess  what  the  law  of  connection  must  be.  When  this 
is  possible,  it  is  found  profitable  to  proceed  deductively, 
reasoning  out  what  consequences  necessarily  follow  from  the 
assumption  of  such  a  general  law.  Of  course,  it  is  essential 
to  verify  results  obtained  in  this  deductive  way  by  compar- 
ing them  with  facts  as  actually  experienced.  The  truth  is 
that  it  is  impossible,  in  actual  thinking,  to  separate  induction 
and  deduction :  the  two  processes  constantly  go  hand  in  hand 
and  are  mutually  supplementary. 

Again,  it  must  be  remembered  that  the  inductive  process, 
considered  broadly  as  the  progressive  interpretation  of  expe- 
rience, is  continuous  throughout.  What  is  already  known  is 
always  taken  as  the  starting-point  for  a  new  investigation. 
And  although  the  immediate  purpose  of  any  special  inquiry 
may  soon  be  satisfied,  the  results  obtained  lead  to  new  ques- 
tions, which  can  be  answered  only  by  further  analysis  and 
investigation.   There  is  then  no  break  — no  fundamental  sep- 


§  53-    Observation  and  Explanation  207 

aration  —  between  the  facts  with  which  induction  starts  and 
the  more  highly  developed  theories  and  generalizations  which 
it  is  sometimes  able  to  reach.  What  we  call  facts  are  them- 
selves the  results  of  former  processes  of  thinking  and  inter- 
pretation, as  well  as  the  starting-point  for  new  analysis  and 
theorizing.  There  is  a  constant  passage  from  one  stage  to  the 
other,  theories  when  approved  and  generally  accepted  coming  to 
be  regarded  as  facts,  and  facts  when  critically  examined  disclos- 
ing the  theoretical  basis  on  which  they  rest.  For  example,  we 
say  that  it  is  a  '  fact '  that  the  earth  revolves  on  its  own  axis. 
Yet  this,  not  very  long  ago,  was  regarded  as  an  '  incredible 
hypothesis.'  And  when  we  reflect,  we  see  that  this  '  fact '  is 
really  a  conception  —  or  a  part  of  a  system  of  conceptions  — 
which  enables  us  to  bring  together  in  our  thought  a  number  of 
simpler  '  facts.'  And  these  latter,  if  examined,  would  in  turn 
prove  to  be  constructed  by  coordinating  and  generalizing 
still  simpler  data,  the  truth  being  that  all  facts  involve  ideas. 

Whewell  has  spoken  of  Induction  as  "  the  true  colligation  of 
facts  by  means  of  an  exact  and  appropriate  conception";  and 
he  goes  on  to  point  out  that  the  distinction  of  fact  and  theory 
is  only  relative.  "  Events  and  phenomena  considered  as  par- 
ticulars which  may  be  colligated  by  Induction,  are  facts; 
considered  as  generalizations  already  obtained  by  colligation 
of  other  facts,  they  are  theories."  i 

§  53.  Observation  and  Explanation.  —  The  Inductive  pro- 
cess being  thus  continuous,  how  are  its  different  stages  to 
be  distinguished  and  classified?  We  may  still  adopt  the 
customary  terms,  and  speak  of  Induction  as  including  both 
Observation,  or  Description,  and  Explanation,  though  it  must 
be  remembered  that  the  one  process  really  involves  the  other. 

1  Novum  Organon  Renovatum,  Bk.  II.,  Aph.  XXIII. 


208  The  Assumptions  of  Induction 

Sometimes  the  relation  between  Observation  and  Explana- 
tion is  stated  in  quite  a  misleading  way.  It  is  said  that  in 
undertaking  an  investigation  we  must  observe  and  describe 
the  facts  as  accurately  as  possible,  and  only  after  this  is  done 
proceed  to  theories  and  explanations.  Now,  as  has  been 
shown,  this  is  to  make  an  artificial  separation  between  col- 
lecting and  describing  the  facts,  and  relating  or  explaining 
them.  As  we  have  seen,  both  processes  go  on  simultaneously. 
The  observation  of  instances  presupposes  some  guiding  idea, 
some  provisional  hypothesis,  perhaps  held  in  the  mind  as  a 
question  to  be  answered.  We  discover  the  relevant  facts  as 
we  go  along  with  our  investigation,  just  as  we  discover  the 
appropriate  conception  or  explanation.  And  just  as  the  facts 
observed  and  described  involve  theories  and  conceptions,  so 
the  explanation  to  which  we  proceed  is  simply  a  fuller  and 
more  accurate  description.  When  the  close  and  necessary 
relation  of  these  stages  of  Induction  is  kept  in  mind,  there  is, 
however,  some  advantage  in  maintaining  the  distinction  be- 
tween Observation  of  the  nature  of  particular  facts  and  the 
wider  organization  of  facts  and  relations  effected  by  what 
we  call  Explanation. 

It  is  the  business  of  the  former  process  to  employ  various 
methods  and  devices  in  order  to  determine  as  accurately  as 
possible  the  nature  of  the  starting-point.  It  is  essential  to  have 
a  full  and  accurate  survey  of  the  terms  of  the  problem^  and 
to  note  carefully  every  clew  that  may  lead  to  its  solution.  In 
the  first  place,  the  different  qualities  of  things  must  be  accu- 
rately observed  and  distinguished.  But  accurate  observation 
in  science  leads  almost  directly  to  the  determination  of  quan- 
titative relations  through  measurement.  Under  this  head  fall 
processes  of  enumeration,  the  measurement  and  recording 


§  53'    Observation  and  Explanation  209 

of  spnce  and  time  relations,  the  determination  of  weights, 
and  the  measurement  of  the  so-called  secondary  qualities  like 
heat,  sound,  and  colour.  The  special  technique  through  which 
such  observations  are  carried  out  and  rendered  precise  in 
the  different  sciences,  must  be  learned  through  occupation 
with  the  actual  phenomena.  In  each  science,  questions  arise 
regarding  methods  of  measurement  —  the  determination  of 
the  units  to  be  employed,  means  of  measuring  indirectly  when 
direct  measurement  is  impossible,  the  most  accurate  method  of 
summing  up  observations  and  of  eliminating  errors  —  as  well 
as  problems  regarding  the  most  convenient  means  of  represent- 
ing quantitative  relations  through  mathematical  formulae, 
graphs,  etc.  In  addition,  the  use  and  manipulation  of  various 
instruments  designed  to  supplement  and  render  more  accu- 
rate the  observations  of  the  senses  have  to  be  learned;  the 
fingers  often  require  to  be  trained  to  perform  delicate  opera- 
tions ;  and  a  special  education  of  the  senses  and  attention  is 
necessary  in  some  fields  before  results  of  scientific  value  can 
be  obtained.  This  technical  knowledge  and  skill  in  the 
employment  of  the  instruments  and  methods  of  observation 
and  description  within  any  science  is  to  be  attained,  as  already 
stated,  only  by  actual  practice.  We  distinguish  practically 
this  work  of  collecting  data  — which  may  be  extended  over 
months  or  years — from  the  construction  of  the  explanatory 
theory,  the  former  often  seeming  to  demand  the  power  of 
patient  observation  and  skill  in  mechanical  manipulation 
rather  than  logical  reasoning. 

It     is    important,    however,    to    remember   that    scientific 
observation  itself  involves  intellectual  activity.    To  observe  — 
at  least  in  the  sense  in  which  the  word  is  used  in  scientific  pro- 
cedure —  requires  something  more  than  the  passive  reception 
p 


210  The  Assumptions  of  Induction 

of  impressions  of  sense  in  the  order  in  which  they  come  to 
us.  Without  some  activity  on  the  part  of  mind,  it  would  be 
impossible  to  obtain  even  the  imperfect  and  fragmentary 
knowledge  of  everyday  life.  But  accurate  observation  is  one 
of  the  means  which  science  employs  to  render  this  know- 
ledge more  complete  and  satisfactory;  and  when  observation 
thus  becomes  an  exact  and  conscious  instrument,  it  involves, 
to  even  a  greater  extent  than  in  ordinary  life,  inteFectual 
activities  like  judgment  and  inference.  It  is  because  this  is 
true,  because  scientific  observation  demands  the  constant 
exercise  of  thought,  in  selecting  and  comparing  the  various 
elements  in  the  material  with  which  it  deals,  that  it  affords 
such  excellent  intellectual  discipline.  The  observational 
sciences  do  not  merely  train  the  sense-organs;  the  discipline 
which  they  afford  is  mental  as  well  as  physiological,  and  it 
is,  of  course,  true  that  mental  training  can  only  be  gained 
through  the  exercise  of  mental  activity. 

(i)  It  is  quite  true  that  it  is  of  the  utmost  importance  to 
distinguish  between  a  fact,  and  further  inferences  from  the  fact. 
As  will  be  pointed  out  in  the  chapter  on  Inductive  Fallacies, 
errors  very  frequently  arise  from  confusing  facts  and  inferences. 
This  does  not  mean,  as  we  have  seen,  that  facts  exist  apart  from 
theories.  But  in  any  particular  case  if  we  would  avoid  confusion, 
we  must  distinguish  sharply  between  the  data  and  further  con- 
structions to  which  we  proceed.  Especially  important  is  it  not  to 
confuse  facts  with  fancies,  or  with  judgments  motived  by  subjec- 
tive feelings.  The  point  which  is  emphasized  in  the  previous 
paragraph,  however,  is  that  it  requires  a  certain  amount  of  think- 
ing in  order  to  get  a  fact  at  all.  Facts  do  not  pass  over  ready- 
made  into  the  mind.  Simply  to  stare  at  things  does  not  give 
us  knowledge:  unless  our  mind  reacts,    judges,    thinks,    we   are 


§  53-    Observation  and  Explanation  211 

not  a  bit  the  wiser  for  staring.  To  observe  well,  it  is  neces- 
sary to  be  more  or  less  definitely  conscious  of  what  one  is  looking 
for,  to  direct  one's  attention  toward  some  particular  field  or  object; 
and  to  do  this  implies  selection  among  the  multitude  of  impressions 
and  objects  of  which  we  are  conscious.  Moreover,  scientific  obser- 
vation requires  analysis  and  discrimination.  It  is  not  unusual,  in 
text-books  on  logic,  to  symbolize  the  various  facts  learned  through 
observation  by  means  of  letters,  a,  b,  c,  etc.,  and  to  take  it  for  granted 
that  they  are  given  in  our  experience  as  distinct  and  separate  phe- 
nomena; but,  as  we  have  just  seen,  judgments  of  analysis  and 
discrimination  are  necessary  to  separate  out  the  so-called  'phenom- 
ena' from  the  mass  or  tangle  of  experience  in  which  they  were 
originally  given.  Again,  to  determine  the  nature  of  a  fact  through 
observation,  it  is  essential  to  note  carefully  how  it  differs  from 
other  facts  with  which  it  is  likely  to  be  confused,  and  also,  to  some 
extent,  what  relations  and  resemblances  it  has.  But  such  know- 
ledge presupposes  that  thought  has  already  been  at  work  in  forming 
judgments  of  comparison. 

(2)  A  distinction  is  sometimes  made  between  observation 
and  experiment.  In  observation,  it  is  said,  the  mind  simply  finds 
its  results  presented  to  it  in  nature,  while  in  experiment  the  answer 
to  a  question  is  obtained  by  actively  controlling  and  arranging  the 
circumstances  at  will.  There  are,  no  doubt,  some  grounds  for 
this  distinction,  though  it  is  not  true  that  the  mind  is  passive  in  the 
one  case,  and  active  in  the  other.  Even  in  observation,  as  we  have 
seen,  knowledge  always  arises  through  active  analysis  and  compari- 
son of  the  instances  selected  as  having  a  bearing  on  some  problem. 
The  difference  is  rather  this :  In  observing,  where  experiment  is  im- 
possible, one  must  wait  for  events  to  occur,  and  must  take  them  in 
the  form  in  which  they  are  presented  in  the  natural  order  of  events. 
But,where  experiment  is  employed,  we  have  control  of  the  conditions, 
and  can  produce  the  phenomena  to  be  investigated  in  any  order,  and 
as  often  as  we  choose.     In  experiment,  as  Bacon  says,  we  can  put 


212  The  Assumptions  of  Induction 

definite  questions  to  nature,  and  compel  her  to  answer.  This  is 
of  course,  an  immense  advantage.  In  some  of  the  sciences,  how- 
ever —  geology  and  astronomy,  for  example  —  it  is  not  possible 
directly  to  control  the  conditions :  one  must  wait  and  observe  the 
results  of  nature's  experiments.  Physics  and  chemistry  are  the 
experimental  sciences  par  excellence;  and,  in  general,  we  may  say 
that  a  science  always  makes  more  rapid  progress  when  it  is  found 
possible  to  call  experiment  to  the  aid  of  observation.  It  is  not 
possible  to  conceive  how  physics  and  chemistry  could  have  reached 
their  present  state  of  perfection  without  the  assistance  of  experiment. 
And  the  rapid  advances  made  in  recent  years  by  biology  and  psy- 
chology have  come  mainly  through  the  introduction  of  experimental 
methods.  Indeed,  the  almost  total  neglect  of  experiment  by  the 
Greek  and  mediaeval  scholars  must  be  regarded  as  one  of  the  chief 
reasons  why  the  physical  sciences  made  so  little  progress  during 
those  centuries. 

We  have  seen  that  the  distinction  between  observation  and 
explanation  is  not  an  absolute  one.  The  task  which  thought 
has  to  perform  —  the  task  which  is  undertaken  by  science  — ■ 
is  to  reduce  the  isolated  and  chaotic  experiences  of  ordinary  life 
to  order  and  system.  And  it  is  important  to  remember  that 
all  the  various  methods  employed  contribute  directly  towards 
this  result.  It  has,  however,  seemed  possible  to  divide  Induc- 
tive methods  into  two  main  divisions.  Observation,  it  was 
said,  seeks  to  discover  the  exact  nature  of  the  facts  to  be  dealt 
with,  and  to  find  accurate  means  of  describing  and  represent- 
ing their  qualitative  and  quantitative  aspects.  But,  when  this 
has  been  accomplished,  we  have  not  by  any  means  reached 
an  end  of  the  matter.  The  desire  for  knowledge  is  not  satisfied 
with  a  mere  statement  of  facts,  or  even  with  a  mathematical 
representation  of  them  in  a  formula  or  a  curve.     Complete 


§  53-    Observation  and  Explanation  213 

Knowledge  demands  an  explanation  of  the  facts  as  determined 
by  the  methods  of  observation.  The  scientist  is  not  content 
to  know  merely  that  such  and  such  phenomena  happen  in  cer- 
tain definite  ways,  but  he  attempts  to  discover  why  this  is  so. 
'  Why,'  we  ask,  '  should  dew  be  deposited  at  certain  times,  or 
water  rise  thirty-two  feet  in  a  pump  ? '  The  demand  is  that 
the  processes  of  analysis  be  pushed  farther  by  thought.  What 
is  requited  is  a  wider  generalization,  or  the  discovery  of  a  more 
general  law  of  behaviour  under  which  the  phenomenon  we 
are  studying  may  fall  as  a  special  case.  Yet  this  explanation, 
when  arrived  at,  is  on  one  side  nothing  more  than  a  more  com- 
plete description  of  the  facts,  calling  attention  to  forces  and 
happenings  that  escape  ordinary  observation.  The  expla- 
nation of  the  pump,  for  example,  called  attention  to  the  weight 
of  the  atmosphere,  hitherto  neglected.  But  the  new  inductive 
step  consists  in  something  more  than  the  addition  of  new  facts. 
What  is  essential  in  explanation  is  rather  the  new  way  of  col- 
ligating or  thinking  the  facts  in  relation  to  one  another, 
afforded  by  the  law  or  conception.  The  difference  between 
Description  and  Explanation  is  obviously  one  of  degree,  being 
simply  a  question  of  how  far  analysis  is  pushed.  In  general, 
we  speak  of  a  conception  as  explanatory  rather  than  descrip- 
tive, when  it  explicitly  brings  different  facts  into  relation. 
Of  course,  Explanation  itself  has  various  degrees  of  complete- 
ness and  ultimateness.  There  always  exists  the  ideal  of  a 
higher  generalization,  a  more  complete  colligation  of  facts 
than  any  which  science  and  philosophy  have  yet  been  able  to 
achieve. 

An  excellent  illustration  of  the  distinction  between  descrip- 
tive and  explanatory  conceptions  is  afforded  by  a  comparison 
of  the  work  of  Kepler  with  that  of  Newton.     Kepler  was  filled 


214  The  Assumptions  of  Induction 

with  the  idea  that  there  must  be  some  relation  capable  of  math- 
ematical expression  between  the  different  positions,  previously 
determined  by  observation,  in  the  orbit  of  the  planet  Mars. 
At  length,  after  trying  and  discarding  numerous  other  hy- 
potheses, he  was  able  to  show  that  an  ellipse  could  be  passed 
through  all  these  points.  The  proof  was  afterwards  worked 
out  of  the  elliptical  character  of  the  orbits  of  the  other  planets. 
The  conception  of  an  ellipse  enabled  Kepler  to  think  all  the 
observed  positions  of  the  planets,  in  relation  to  one  another. 
But  the  explanation  of  why  the  planets  moved  through  ellip- 
tical orbits  was  still  lacking.  That  explanation,  as  is  well 
known,  was  given  by  Newton  in  his  conception  of  universal 
gravitation.  This  was  explanatory  because  it  linked  together 
the  movements  of  the  planets  with  the  behaviour  of  all  other 
bodies  moving  in  space,  thus  enabling  the  former  to  be 
thought  as  examples  or  instances  of  the  action  of  a  universal 
principle. 

It  is  usually  said  that  where  we  know  merely  the  nature  of  phe- 
nomena, and  their  connection,  without  being  able  to  explain  these 
facts,  our  knowledge  is  empirical.  Thus,  I  may  know  that  an  ex- 
plosion follows  the  contact  of  a  lighted  match  with  gunpowder,  or 
that  a  storm  follows  when  there  is  a  circle  around  the  moon,  without 
being  able  to  explain  in  any  way  why  these  facts  are  connected. 
On  the  other  hand,  if  we  can  connect  events  by  showing  the  gen- 
eral principle  involved,  we  say  that  our  knowledge  is  really  scientific. 
It  is  important  to  notice,  however,  that  empirical  knowledge  is  simply 
in  a  less  advanced  stage  than  the  scientific  knowledge  which  has  suc- 
ceeded in  gaining  an  insight  into  the  general  law;  and  also  that 
any  knowledge  might  be  called  empirical,  when  contrasted  with  a 
more  complete  explanation.  Thus  Kepler's  knowledge,  that  the 
orbits  of  the  planets  are  ellipses,  was  empirical  compared  with  that 


§  53-    Observation  and  Explanation  215 

ci  Newton.  Empirical  knowledge  leaves  a  problem  which  intelli- 
gence has  still  to  solve.  It  is,  of  course,  true  that  a  large  part  of 
every  one's  knowledge  is  empirical  in  character.  We  all  know 
many  things  which  we  cannot  explain.  In  all  the  sciences,  too, 
phenomena  are  met  with  which  seem  to  defy  all  attempts  at  expla- 
nation. Indeed,  some  of  the  sciences  can  scarcely  be  said  to  have 
passed  the  empirical  stage.  The  science  of  medicine,  for  example, 
has  hardly  yet  reached  any  knowledge  of  general  principles.  The 
physician  knows,  that  is,  as  a  result  of  actual  experiment,  that 
such  and  such  drugs  produce  such  and  such  effects.  But  he 
knows  almost  nothing  of  the  means  by  which  this  result  is  achieved, 
and  is  therefore  unable  to  go  beyond  the  fact  itself.  In  this  respect, 
he  is  very  little  better  off  than  the  ordinary  man,  who  knows  that 
if  he  eats  certain  kinds  of  food  he  will  be  ill,  or  if  he  drinks  strong 
liquors  in  excess  he  will  become  intoxicated. 

REFERENCES  TO  CHAPTERS  XIII  AND  XIV 

C.  Sigwart,  Logic,  Vol.  II.,  Ch.  V. 
B.  Bosanquet,  Logic,  Vol.  II.,  Chs.  II.-V. 

H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Chs.  XVIII.  and  XIX. 
W.  Whewell,  Novum  Organon  Renovatum. 
L.  H.  Hobhouse,  The  Theory  of  Knowledge,  Chs.  XI.-XIV. 
W.  P.  Montague,  "  On  the  Nature  of  Induction,"  Journal  of  Philos 
and  Psych.,  Vol.  III.,  pp.  281  ff. 


CHAPTER    XV 

ENUMERATION   AND   STATISTICS 

§  54.  Enumeration  or  Simple  Counting. —  We  shall  begin 
the  account  of  the  scientific  methods  with  Enumeration.  To 
count  the  objects  which  we  observe,  and  to  distinguish  and  num- 
ber their  parts,  is  one  of  the  first  and  most  essential  operations 
of  thought.  It  is  of  course  true  that  qualitative  distinctions 
generally  precede  quantitative.  The  child  learns  to  distin- 
guish things  by  some  qualitative  mark,  such  as  'black'  or 
'hot,'  before  he  is  able  to  count  them  (cf.  §  87).  We  may 
say,  however,  that  the  qualities  of  things  are  known,  in  a 
general  way  at  least,  before  scientific  procedure  begins.  The 
determination  of  quantity,  on  the  other  hand,  seems  to 
demand  a  more  conscious  effort  on  the  part  of  the  mind.  We 
learn  to  distinguish  the  general  qualities  of  things  without 
effort;  but,  in  order  to  obtain  quantitative  knowledge,  it  is 
necessary  to  set  ourselves  deliberately  to  work.  And  it  is  also 
necessary,  as  we  shall  see,  to  decide  what  we  shall  count.  We 
must  make  up  our  mind,  with  some  general  idea  more  or  less 
consciously  before  us,  what  it  is  worth  while  to  enumerate. 
We  may,  accordingly,  take  Enumeration,  or  Simple  Count- 
ing, which  is  perhaps  the  easiest  kind  of  quantitative 
determination,  as  our  starting-point  in  dealing  with  the 
Inductive  Methods. 

A  considerable  step  in  advance,  in  the  task  of  reducing  the 

216 


§  54-    Enumeration  or  Simple  Counting  217 

world  of  our  experience  to  order  and  unity,  is  taken  when  we 
begin  to  count,  i.e.  to  group  together  things  of  the  same  kind, 
and  to  register  their  number.  Thus  Enumeration  is,  to  some 
extent,  also  a  process  of  classification.  What  is  counted  is 
always  a  collective  whole,  the  units  of  which  are  either  all  of 
the  same  kind,  or  else  belong  to  a  limited  number  of  differ- 
ent classes.  Thus  one  might  determine  by  Enumeration  the 
number  of  sheep  in  a  flock,  taking  each  individual  as  belonging 
to  the  same  general  class,  '  sheep ';  or  the  analysis  might  be 
pushed  farther  so  as  to  give  as  a  result  the  number  of  white  and 
of  black  sheep  separately.  The  purpose  for  which  the  enu- 
meration is  undertaken  always  determines  the  length  to  which 
the  process  of  analysis  and  distinction  is  carried.  For  example, 
if  the  object  of  a  census  enumeration  were  simply  to  determine 
the  number  of  inhabitants  in  a  country,  it  would  not  be  neces- 
sary to  make  any  distinctions,  but  each  person  would  count  as 
one.  But  where,  as  is  often  the  case,  the  aim  is  not  simply  to 
count  the  sum-total,  but  also  to  determine  the  relative  numbers 
belonging  to  various  classes,  analysis  has  to  be  pushed  further. 
In  such  cases,  we  might  count  the  number  belonging  to  each 
sex,  the  native-born,  and  those  of  foreign  birth,  those  below, 
and  those  above  any  given  age,  etc. 

In  the  last  chapter  we  have  seen  that  the  so-called  '  Perfect 
Induction,'  where  all  instances  are  examined,  is  not  properly 
called  Induction  at  all,  since  there  is  no  inference  to  anything 
new.  Scientific  Induction  analyzes,  notes  special  accompany- 
ing circumstances,  and  gets  beneath  the  surface  to  the  real  or 
essential  happening  in  the  various  cases.  But  we  saw  that 
before  the  process  of  analysis  is  carried  out,  as  well  as  in  cases 
where  the  conditions  are  too  complex  or  difficult  to  determine, 
we  do  proceed  to  generalize  with  greater  or  less  confidence  on 


218  Enumeration  and  Statistics 

the  basis  of  the  instances  observed.  If  instances  of  P  and  Q. 
for  example,  have  always  been  found  in  conjunction,  and  if  we 
are  confident  that  there  has  been  nothing  limiting  or  restrict- 
ing observation  to  some  special  type  of  instance,  we  assume 
that  the  connection  is  not  a  mere  'casual  coincidence,'  but 
that  in  some  form  it  holds  universally.  In  such  cases,  the 
number  of  instances  —  provided  they  can  be  assumed  to  be 
really  unrestricted  —  does  seem  to  have  a  bearing  on  the  logical 
character  of  the  conclusion.  The  connection  P  —  Q  is  less 
likely  to  be  merely  'casual'  in  proportion  to  the  frequency 
with  which  '  free,  or  unrestricted '  cases  of  it  are  observed,  while 
at  the  same  time  no  exceptions  to  it  appear.  The  '  imperfect ' 
character  of  the  Induction,  when  based  on  a  number  of  care- 
fully established  instances  that  show  no  exception  throughout 
a  considerable  range,  is  found  rather  in  the  fact  that  thenature 
of  the  connection  P  —  Q  is  left  vague  and  undetermined,  than 
in  any  lack  of  certainty  regarding  the  existence  of  some 
universal  principle  of  relationship.  The  invariable  conjunc- 
tion of  a  number  of  '  free '  instances  rules  out  the  assumption 
of  'chance';  but,  in  so  far  as  the  instances  are  left  unana- 
lyzed,  the  precise  form  of  the  universal  mode  of  connection 
is  not  exhibited  in  and  through  them. 

Where  experience  shows  both  positive  and  negative  cases, 
and  where  at  the  same  time  it  is  impossible  to  discover  any 
basis  of  difference  for  the  two  sets  of  results,  we  can  compare 
the  number  of  instances  in  which  the  connection  obtains  with 
that  in  which  it  fails.  The  ratio  thus  obtained  may  then  be 
made  the  basis  for  calculating  the  probability  of  any  particular 
event;  or  even  of  determining  the  likelihood  that  there  is  some 
law  operative  with  regard  to  the  observed  phenomena  (cf. 
P-  232). 


§  54-    Enumeration  or  Simple  Counting  219 

As  a  matter  of  fact,  however,  Enumeration  of  instances  is 
an  aid  to  Induction  mainly  because  in  actual  counting  classifi- 
cation and  analysis  are  also  being  effected.  We  are  never 
content  merely  to  count,  taking  each  barely  as  'one  instance.' 
We  also  take  account  of  the  character  of  the  instances,  reject- 
ing those  that  are  not '  fair'  or '  typical'  and  emphasizing  others 
as  of  special  or  'prerogative'  importance.  Moreover,  the 
assemblage  of  instances  of  different  types  —  of  connection 
and  lack  of  connection,  of  different  races,  or  ages,  etc.,  serves 
to  bring  out  differences  and  similarities  between  groups.  In 
other  words,  statistics,  when  collected  intelligently  and  with 
some  problem  in  view,  are  really  instruments  of  analysis;  and 
in  fields  where  experimentation  is  not  possible,  they  may  be 
capable  of  revealing,  not  merely  the  fact  that  certain  groups 
of  things  are  correlated,  but  also  to  some  extent  the  character 
of  that  correlation. 

The  conclusion  which  we  reach,  then,  is  that  no  process  of 
enumeration  has  any  claim  to  the  title  of  Perfect  Induction. 
Enumeration  is  the  beginning,  rather  than  the  end  of  the  induc- 
tive procedure.  Nevertheless,  it  is  exceedingly  useful  as  a  pre- 
liminary step  and  preparation  for  scientific  explanation.  The 
number  of  stamens  and  pistils  which  a  plant  contains,  or  the 
number  of  tympanic  bones  possessed  by  an  animal,  is  often  of 
the  greatest  service  in  classification.  And  classification, 
although  it  is  by  no  means  the  end  of  scientific  investigation, 
is  in  many  of  the  sciences  a  most  essential  and  important  step 
toward  that  end.  The  task  of  explaining  the  infinite 
variety  of  natural  objects  would  be  a  hopeless  one,  if  it  were 
not  possible  to  discover  similarities  of  structure,  in  virtue  of 
which  things  can  be  grouped  together  in  classes.  To  this, 
enumeration  in  a  very  great  degree  contributes,  especially  if 


220  Enumeration  and  Statistics 

the  counting  is  accompanied  and  directed  by  methodical 
thinking,  so  that  the  likenesses  and  characteristics  enumerated 
are  not  taken  at  haphazard,  but  are  really  important  ones,  and 
such  as  to  bring  out,  by  means  of  the  classification,  answers 
to  definite  questions.  Enumeration  thus  not  merely  groups 
together  the  phenomena  to  be  studied  in  a  compact  form,  but 
at  the  same  time  begins  the  process  of  analysis,  revealing 
resemblances  and  differences. 

§  55.  Statistics  and  Statistical  Methods.  — Statistical  meth- 
ods depend  upon  enumeration.  They  aim  at  making  the 
process  of  counting  as  exact  and  precise  as  possible.  Riimelin 
defines  statistics  as  "the  results  obtained  in  any  field  of  reality 
by  methods  of  counting."  Modern  science  has  come  to  under- 
stand that  its  first  task  must  be  to  become  acquainted,  as  com- 
pletely as  possible,  with  the  nature  of  the  facts  presented  to  it 
by  experience.  And,  for  this  purpose,  the  careful  classification 
and  precise  enumeration  of  particulars  afforded  by  statistics 
is  often  of  the  greatest  importance.  "The  extent  to  which  the 
statistical  method  prevails,  and  everything  is  counted,"  says 
Professor  Sigwart,  "is  another  instance  of  the  fundamental 
difference  between  ancient  and  modern  science."  l  It  would, 
of  course,  be  impossible  to  enter  here  into  a  full  description  of 
the  methods  employed  by  statistical  science.  The  methodol- 
ogy of  every  science  must  be  learned  by  actual  practice  within 
the  particular  field.  What  we  are  interested  in  from  a  logical 
point  of  view  is  the  purpose  which  statistical  investigation 
seeks  to  fulfil,  and  the  part  which  it  plays  in  rendering  our 
knowledge  exact  and  systematic. 

We  notice,  in  the  first  place,  that  the  class  of  facts  to  which 
statistics  are  applied  has  two  main  characteristics:  the  subject 

1  Logic  (Eng.  trans.),  Vol.  I.,  p.  286. 


§  55-    Statistics  and  Statistical  Methods  221 

dealt  with  is  always  complex,  and  capable  of  division  into  a 
number  of  individual  parts  or  units;  and,  secondly,  it  is  also 
of  such  a  nature  that  the  underlying  law  or  principle  of  the 
phenomena  to  be  investigated  cannot  be  directly  discovered. 
Thus,  we  employ  statistics  to  determine  the  death-rate  of  any 
country  or  community,  or  the  ratio  between  the  number  of 
male  and  of  female  births.  It  is  clear  that  it  is  impossible  to 
make  use  of  experiment  when  we  are  dealing  with  facts  of  this 
kind,  because  the  conditions  are  not  under  our  control.  If  it 
were  possible,  for  example,  to  determine  exhaustively  the 
general  laws  according  to  which  the  various  meteorological 
changes  are  coordinated  with  their  conditions,  we  should  not 
trouble  ourselves  to  count  and  register  the  separate  instances 
of  changes  in  the  weather.  Nor,  if  we  knew  exactly  the  general 
conditions  under  which  any  given  human  organism  in  contact 
with  its  environment  would  cease  to  exist,  should  we  count 
the  individual  cases  of  death.  "  In  proportion  as  we  are  un- 
able to  reduce  the  particular  event  to  rules  and  laws,  the 
numeration  of  particular  objects  becomes  the  only  means  of 
obtaining  comprehensive  propositions  about  that  which  is, 
for  our  knowledge,  fortuitous;  as  soon  as  the  laws  are  found, 
statistical  numeration  ceases  to  be  of  interest.  There  was 
some  interest  in  counting  how  many  eclipses  of  the  moon  and 
sun  took  place  year  by  year,  so  long  as  they  occurred  unex- 
pectedly and  inexplicably;  since  the  rule  has  been  found 
according  to  which  they  occur,  and  can  be  calculated  for 
centuries  past  and  to  come,  that  interest  has  vanished.  But 
we  still  count  how  many  thunder-storms  and  hail-storms 
occur  at  a  given  place,  or  within  a  given  district,  how  many 
persons  die,  and  how  many  bushels  of  fruit  a  given  area  pro- 


222  Enumeration  and  Statistics 

duces,  because  we  are  not   in  a  position  to  calculate  these 
events  from  their  conditions."  ' 

In  cases  like  those  mentioned  above,  where  we  are  as  yet 
unable  to  determine  the  general  laws  which  are  at  work,  we 
call  to  oui  aid  statistical  enumeration.  There  are  three  main 
advantages  to  be  derived  from  ihe  employment  of  this  method. 
In  the  first  place,  it  contributes  directly  towards  a  clear  and 
comprehensive  grasp  of  the  facts.  Instead  of  the  vague  im- 
pression derived  from  ordinary  observation,  statistics  enable 
us  to  state  definitely  the  proportion  of  fine  and  rainy  days 
during  the  year.  Statistical  enumeration  is  thus  one  of  the 
most  important  means  of  rendering  observation  exact  and 
trustworthy,  and  of  summing  up  its  results  in  a  convenient 
and  readily  intelligible  form.  It  is  of  the  utmost  importance, 
when  dealing  with  complex  groups  of  phenomena,  to  have  a 
clear  and  comprehensive  view  of  the  facts  of  the  case.  Thus, 
when  trying  to  understand  the  nature  of  society,  it  is  neces- 
sary to  determine  accurately,  by  means  of  statistics,  such 
facts  as  the  number  of  male  and  of  female  births,  the  death- 
rate,  the  proportion  of  marriages,  the  age  of  marriage,  etc. 
This  may  be  regarded  as  the  descriptive  use  of  statistics.  In 
the  second  place,  by  giving  us  the  average  in  the  past  for 
large  numbers  of  things  or  events  occurring  within  certain 
lengths  of  time,  in  areas  of  space,  statistics  enable  us  to  form 
probable  judgments  as  to  what  will  happen  in  the  future  in 
cases  where  we  cannot  predict  because  the  causal  laws  are 
unknown  or  are  too  complex.  This  second  use  will  be  dis- 
cussed in  §  56.  But,  in  the  third  place,  statistics  often  serve 
to  reveal  quantitative  correspondences  or  uniformities  be- 
tween two  groups  of  phenomena,  and  thus  suggest  that  some 

1  Sigwart,  Logic  (Eng.  trans.),  Vol.  II.,  p.  483. 


§  55-    Statistics  and  Statistical  Methods  223 

causal  connection  exists  between  them.  It  is  found,  for  ex- 
ample, that  the  number  of  births  in  any  given  country  varies 
inversely  as  the  price  of  food  during  the  previous  year.  Now, 
this  fact  at  once  suggests  the  existence  of  certain  physio- 
logical and  psychological  laws  which  may  serve  to  bring 
these  facts  into  causal  relation.  In  many  cases,  such  cor- 
respondences serve  only  to  confirm  our  expectation  of  the 
presence  of  a  causal  law,  which  is  based  on  other  grounds. 
Thus  we  should  naturally  expect  that  there  would  be  a  rela- 
tively greater  number  of  cases  of  fever  in  a  town  which  had 
an  insufficient  water  supply,  or  an  antiquated  system  of  sew- 
erage, than  in  a  town  where  these  matters  were  properly  pro- 
vided for  ;  and  statistics  might  bear  out  our  conclusions.  In 
general,  however,  it  may  be  said  that  causal  laws  are  sug- 
gested, not  by  corresponding  uniformities,  but  by  correspond- 
ing variations,  as  shown  by  the  statistics  of  different  sets  of 
facts.  So  long  as  the  death-rate,  for  example,  shows  a  con- 
stant ratio  to  the  population,  no  causal  inference  is  suggested; 
but  if  the  annual  number  of  deaths  increases  or  decreases 
considerably,  we  are  led  to  look  for  some  variation  from  the 
normal  in  some  coincident  group  of  phenomena.  And  if  it 
is  found  that  the  variation  in  the  death-rate  has  been  accom- 
panied by  unusually  favourable  or  unfavourable  conditions 
of  weather,  the  presence  or  absence  of  epidemics,  or  any 
similar  circumstances,  there  will  be  at  least  a  presumption  that 
a  causal  relation  exists  between  these  two  sets  of  events.  — 
From  a  certain  likeness  or  quantitative  proportion  between 
the  variations  of  two  distinct  classes  of  phenomena,  we  are 
led  to  the  hypothesis  of  their  causal  connection. 

In  this  use  of  statistics,  they  become  directly  auxiliary  to  an 
explanation  of  the  facts  they  enumerate.     But  the  correlation 


224  Enumeration  and  Statistics 

md  causal  connection  of  the  facts  come  to  light  only  when 
looked  for.  Merely  to  count,  without  any  definite  purpose, 
would  never  help  us  to  explain.  As  we  saw  in  the  last  chapter, 
induction  always  proceeds  under  the  guidance  of  conceptions 
or  general  ideas.  We  do  not  simply  stare,  as  it  were,  at  the 
facts  we  examine,  but  we  look  at  them  to  discover  their 
meaning  and  select  such  of  them  as  are  relevant  or  significant 
in  the  light  of  some  general  theory  or  conception.  In  other 
words,  we  examine  the  facts  to  put  theories  (which  may,  of 
course,  be  very  vague  as  yet)  to  the  test,  or  to  get  answers  to 
certain  questions  which  we  have  in  mind.  Now  this  is  just 
as  true  of  enumeration  and  statistics  as  it  is  of  the  other 
methods  of  induction.  As  has  already  been  remarked  of 
enumerative  classification,  we  must  decide  what  it  is  worth 
while  to  count  in  the  particular  field  in  which  we  are  count- 
ing. The  questions  that  we  wish  answered  will  determine 
this.  And  even  when  we  have  our  figures,  they  will  be 
meaningless  or  even  altogether  misleading  unless  we  know 
how  to  interpret  them.  It  is  the  neglect  of  such  considera- 
tions that  leads  to  the  misuse  of  statistics  and  the  frequent 
contradiction  of  the  statement  that  '  figures  cannot  lie.' 

(i)  It  is  true  that  on  a  superficial  view  of  the  statistical  method 
the  figures  may  seem  at  times  to  arrange  themselves  in  definite 
groups  quite  apart  from  any  intellectual  labour  save  that  of  mere 
counting.  Thus  it  might  seem  that  in  taking  the  average  rate  of 
mortality  on  the  basis  of  the  returns  of  local  officials,  etc.,  the 
figures  of  themselves  disclosed  the  fact  that  the  rate  was  higher  for 
infants  under  two  years  of  age  than  in  later  periods  of  life.  But 
the  total  average  of  deaths  would  never  have  shown  this.  It  is  only 
because  the  average  for  infants  has  been  separately  calculated,  in 
the  expectation  that  there  might  be  a  difference,  that  the  different 


§  55-    Statistics  and  Statistical  Methods  225 

zias  been  found.  The  tentative  question  —  Is  there,  as  we  have 
reason  on  the  ground  of  unsystematic  observation  to  believe,  a 
striking  difference  between  the  death-rate  of  infants  and  that  of 
older  persons  ?  —  is  thus  answered  in  the  affirmative. 

But  the  function  of  guiding  ideas  and  hypotheses  becomes  even 
more  important  when  the  statistics  are  to  be  used  directly  in  the 
service  of  explanation.  Two  examples  will  serve  to  make  this 
plain.  The  first  is  from  Professor  Sigwart:  "The  position  of  a 
barometer  in  a  given  locality  passes  from  day  to  day,  and  from 
month  to  month,  up  and  down  through  all  possible  variations,  in 
which  we  can  at  first  find  absolutely  no  rule  (though  they  have  a 
constant  mean  value).  .  .  .  But  if  we  calculate  the  average  for  the 
particular  hours  of  the  day  over  a  considerable  time,  we  find  a 
periodical  variation  between  two  maxima  and  minima  with  respect 
to  the  general  average.  .  .  .  That  the  period  is  daily  points  to 
the  influence  of  the  sun.  .  .  .  But  unless  we  had  conjectured 
that  the  different  positions  of  the  sun,  and  the  changes  brought 
about  by  them,  had  some  influence,  we  could  not  have  thought  of 
summing  up  the  particular  hours  of  the  day  apart  from  each 
other."1  In  this  case,  the  constant  average  first  obtained  told  us 
nothing,  except  that  the  conditions,  whatever  they  were,  which 
governed  the  fluctuations  of  the  barometer,  remained  constant  on 
the  whole.  But  when  an  hypothesis  was  found,  and  the  varying 
positions  divided  into  groups  of  such  a  nature  that  their  com- 
parison could  test  it,  we  obtained  a  partial  explanation  of  them. 

Again,  suppose  that  we  are  gathering  statistics  of  the  divorce- 
rate  in  various  states  and  countries.  The  figures,  unanalyzed, 
would  tell  us  little.  But  suppose  we  had  a  definite  problem  in 
mind,  such  as  the  effect  of  laws  on  the  frequency  of  divorce.  What 
would  we  do  with  our  figures?  "First,  select  states  or  countries 
with  similar  social  and  economic  conditions,  but  very  different 
laws,  and  compare  their  divorce-rate;    do  the  same  for    states 

1  Logic,  Eng.  trans.,  Vcl.  II.,  pp.  .'06-497. 


226  Enumeration  and  Statistics 

with  similar  laws,  but  different  economic  conditions ;  note  whether 
the  divorce-rate  varies  with  the  law,  or  with  the  other  factors,  or 
with  neither  exclusively.  Secondly,  examine  every  instance  of  a 
change  in  the  divorce  law,  and  observe  whether  it  was  attended  by 
a  change  in  the  figures  such  as  might  have  been  produced  by  the 
law."1  Here  again  there  is  a  division  of  the  phenomena  into 
groups  distinguished  by  some  difference  in  the  supposed  cause, 
and  then  a  comparison  of  these  groups.  The  methods  employed, 
as  we  shall  see  presently,  are  essentially  those  of  Agreement  and 
Difference,  and  of  Concomitant  Variations. 

In  general,  then,  there  are  two  things  to  be  said  about  the  use  of 
statistics.  In  the  first  place,  the  smaller  and  more  numerous  the 
groups  are  into  which  the  enumerated  phenomena  are  divided,  and 
the  more  exactly  the  rules  of  division  in  general  are  followed  in 
doing  this,  the  more  valuable,  other  things  being  equal,  the  statistics 
will  be.  In  the  second  place,  it  is  by  the  comparison  of  these 
groups  that  statistics  aid  us  to  discover  causal  relations.  The 
kind  of  groups  we  shall  make,  and  the  points  in  which  we  shall 
compare  them,  are  determined  by  the  questions  we  have  to  ask,  or 
the  tentative  conceptions  we  have  to  test.  In  all  these  respects 
the  use  of  statistics  is  governed  by  the  general  principles  of  the 
inductive  method,  which  consists  essentially  in  the  analysis  and 
comparison  of  phenomena  in  the  light  of  an  hypothesis. 

(2)  Statistical  enumeration  is  frequently  employed  to  determine 
the  average  of  a  large  number  of  instances  of  a  particular  kind.  This 
is  obtained  by  dividing  the  sum  of  the  given  numbers  by  the  num- 
ber of  individuals  of  which  account  is  taken.  In  this  way  a  general 
average  is  reached  which  does  not  necessarily  correspond  exactly 
with  the  character  of  any  individual  of  the  group.  It  represents  a 
purely  imaginary  conception,  which  omits  individual  differences  and 
presents  in  an  abbreviated  form  the  general  character  of  a  whole 
class  or  group.     In  this  way,  by  the  determination  of  the  average,  it 

1  Willcox,  The  Divorce  Problem,  p.  41. 


§  55-    Statistics  and  Statistical  Methods  227 

becomes  easier  to  compare  complex  groups  with  one  another.  Thus, 
when  the  average  height  of  Frenchmen  and  Englishmen  has  been 
determined,  comparison  is  at  once  made  possible.  From  the  mean 
or  average  of  a  number  of  individuals,  or  set  of  instances,  however, 
we  can  infer  nothing  regarding  the  character  of  any  particular  indi- 
vidual, or  of  any  particular  instance.  What  is  determined  by  the 
method  of  averages  is  the  general  nature  of  the  group,  as  represented 
by  the  average  or  typical  individual.  But  this  method  does  not 
enable  us  to  infer  anything  regarding  the  character  of  any  member 
of  the  group,  A,  or  B. 

Indeed,  the  simple  arithmetical  mean  or  average  by  itself  may 
give  us  quite  an  erroneous  idea  of  the  general  character  of  the  indi- 
viduals or  instances  which  make  up  the  group.  For  example,  if 
ten  divorces  were  granted  in  a  county,  eight  at  the  end  of  three 
years  of  married  life,  one  at  the  end  of  six,  and  one  at  the  end 
of  thirty,  it  would  give  quite  a  misleading  notion  to  say  that  the 
average  duration  of  marriage  in  couples  seeking  divorce  there  was 
six  years.  In  order  to  correct  such  defects  in  the  use  of  the  average 
by  itself,  especially  in  applying  the  statistical  method  in  biology, 
two  other  expressions  are  now  used,  the  mode  and  the  median 
value.  The  mode  is  the  condition  which  occurs  most  often  in  the 
group  examined;  in  the  example  just  cited  it  would  be  three  years. 
The  median  value  is  the  condition  of  the  individual  at  the  middle 
of  the  series,  when  it  is  arranged  in  order.  In  this  case  it  approx- 
imates to  the  mean.  When  the  group  is  symmetrically  distributed 
about  the  average,  these  three  expressions  are  approximately  the 
same ;  but  as  it  becomes  less  evenly  distributed,  they  differ  more  or 
less  widely,  and  now  one  of  them,  now  the  other,  may  give  a  better 
notion  of  the  character  of  the  group  than  the  average  by  itself 
would.  All  three  expressions,  however,  are  primarily  expressions 
for  the  general  nature  of  the  group;  and  the  information  they 
give  us  concerning  the  nature  of  any  individual  member  of  it  is 
always  indirect,  imperfect,  and  uncertain,  save  as  we  are  informed 


228  Enumeration  and  Statistics 

where  in  the  group  the  member  occurs.     There  are  also  occasion? 
when  it  is  preferable  to  use  the  geometrical  mean. 

§  56.  The  Calculation  of  Chances.  — We  still  have  to  con- 
sider the  second  of  the  three  uses  of  statistics  mentioned  in 
the  foregoing  section.  As  has  been  said,  statistics  not  only 
help  us  in  describing  and  in  explaining  complex  phe- 
nomena, but  they  are  also  used  to  enable  us  to  judge  what 
will  be  true,  on  the  whole,  of  a  long  series  of  events,  in  cases 
where  ignorance  of  the  causal  laws  concerned  prevents  our 
making  predictions  concerning  the  individual  members  of 
the  series,  when  taken  separately.  This  is  usually  called 
the  calculation  of  chances,  or  probabilities.  Now  there  is, 
of  course,  no  such  thing  as  'chance,'  regarded  as  a  power 
which  controls  and  governs  events.  When  we  speak  of  some- 
thing happening  'by  chance,'  or  of  some  occurrence  as 
'  probable,'  we  are  expressing  merely  a  deficiency  in  our  own 
knowledge.  "There  is  no  doubt  in  lightning  as  to  the  point  it 
shall  strike;  in  the  greatest  storm  there  is  nothing  capricious; 
not  a  grain  of  sand  lies  upon  the  beach  but  infinite  knowledge 
would  account  for  its  lying  there;  and  the  course  of  every 
falling  leaf  is  guided  by  the  same  principles  of  mechanics  as 
rule  the  motions  of  the  heavenly  bodies."  !  To  assert  that 
anything  happens  by  chance,  then,  is  simply  to  confess  our 
ignorance  of  the  causes  which  are  operative. 

It  is  clear  that  we  are  in  this  position  regarding  many  of 
the  ordinary  events  which  belong  to  the  future.  Because 
of  my  ignorance  of  the  causes  at  work,  I  can  only  say,  '  It 
may  rain  to-morrow.'  It  is  impossible  to  tell  upon  which 
side  a  penny  will  fall  at  any  particular  throw,  or  what  card 
may  be  drawn  from  a  pack.     But  in  cases  like  these,  we  have 

1  Jevons,  The  Principles  of  Science,  Vol.  I.,  p.  225. 


§  56.    The  Calculation  of  Chances  229 

to  accept,  for  lack  of  anything  better,  a  numerical  statement 
of  the  chances  for  any  particular  event.    Thus  we  know 
that,  since  there  are  only  two  sides  upon  which  a  penny  can 
fall,  the  chances  of  throwing  heads  in  any  trial  is  \.     Simi- 
larly, there  are  four  chances  out  of  fifty-two  of  drawing  an 
ace  from  a  pack  of  cards.    The  chance  of  obtaining  an  ace 
by  any  draw  is  therefore  -fe  =  TV    These  figures  express  the 
mathematical  chances.     Experience  of  a  limited  number  of 
instances  may,  however,  sometimes  appear  to  show  a  lack 
of  harmony  between  the  mathematical  and  the  actual  chances. 
But  in  proportion  as  the  number  of  trials  is  increased,  the 
result  is  found  to  approximate  more  and  more  nearly  to  the 
mathematical  expectation.     In  twenty  throws  of  a  penny 
or  a  die,  we  should  not  be  surprised  to  find  that  the  result 
differed    from    the    fraction    expressing    the    mathematical 
chances.     But  this  discrepancy  would  tend  to  disappear  as 
the  number  of  cases  was  increased.     Jevons  illustrated  this 
by  actual  trial,  using  a  number  of  coins  at  a  time.     Out 
of  a  total  of  20,480  throws,  he  obtained  a  result  of  10,353 
heads.    On  the  result  of  the  experiment  he  remarks:    "The 
coincidence   with    theory    is   pretty   close,    but    considering 
the  large  number  of  throws  there  is  some  reason  to  suspect 
a  tendency  in  favour  of  heads."  x 

Apart  from  the  simple  and  somewhat  artificial  cases 
where  we  are  concerned  with  coins  and  dice,  etc.,  it  is  impos- 
sible to  determine  with  mathematical  precision  the  chances 
for  or  against  any  event,  since  the  possibilities  are  indefinite 
as  well  as  the  causes.  In  cases  where  the  whole  series  of 
possibilities  does  not  lie  before  us,  we  have  to  base  our  cal- 
culations for  the  future  on  what  is  known  regarding  the  fre- 

1  Jevons,  op.  cit.,  Vol.  I.,  p.  230. 


230  Enumeration  ana  Statistics 

quency  with  which  the  events  under  consideration  have 
occurred  in  the  past.  Now  the  results  of  the  last  paragraph 
make  it  clear  that  it  is  of  the  utmost  importance  that  the 
statistics,  which  are  taken  as  the  basis,  shall  be  as  full  and 
comprehensive  as  possible.  It  is  evident,  for  example,  that 
serious  errors  would  be  likely  to  arise,  if  the  death-rate  for 
a  single  year,  or  for  a  single  county  or  town,  were  taken 
as  typical  of  the  country  as  a  whole.  To  render  statistics 
trustworthy,  they  must  be  extended  over  a  considerable 
period  of  time,  and  over  a  large  extent  of  country,  so  as  to 
eliminate  the  accidents  due  to  a  particular  time  or  to  a 
particular  locality. 

(1)  When  this  has  been  done,  however,  and  statistics  have  been 
obtained  that  have  a  right  to  be  regarded  as  really  typical,  the 
chances  in  any  individual  instance  regarded  simply  as  one  member 
of  a  large  group,  and  apart  from  its  own  special  characteristics,  can 
be  readily  shown.  Thus  we  find  that  out  of  one  thousand  children 
born,  about  two  hundred  and  fifty  die  before  the  age  of  six  years. 
The  chances,  then,  at  birth,  that  any  child  will  reach  this  age,  are 
tto°o  or  I-  Again,  it  is  found  that  only  about  two  persons  in  one 
thousand  live  to  be  ninety  years  old.  So  that  the  probability  of 
any  child  living  to  this  age  would  be  expressed  by  the  fraction  y^Vff 
or  -5^.  Such  probabilities  are  simply  averages  which  briefly  de- 
scribe what  has  happened  in  the  past.  Now  what  has  happened  in 
the  past  in  a  large  number  of  cases  we  naturally  expect  to  happen 
in  the  future.  This  is  essentially  the  principle  upon  which  life- 
insurance  companies  proceed.  Their  business  is  conducted  on 
the  assumption  that  there  will  be  an  approximately  constant 
death-rate,  though  they  cannot  foretell  what  particular  individuals 
are  to  die  in  any  year.  It  thus  becomes  possible  to  calculate 
what  losses  from  death  may  be  expected  each  year.  Suppose 
that  it  is  found  that  the  annual  death-rate  among  men  of  a  certain 


§  $6.    The  Calculation  of  Chances  231 

age  throughout  the  country  is  twenty  out  of  every  thousand.  If 
each  man's  life  were  insured  for  $1000,  the  loss  to  the  company 
from  this  source  would  be  $20,000.  To  compensate  for  this  loss, 
the  company  would  be  obliged  to  demand  an  annual  payment  of 
$20  from  each  of  the  one  thousand  individuals  in  the  class.  Of 
course,  the  actual  computations  upon  which  insurance  is  based 
in  concrete  cases  are  vastly  more  complex  than  this,  and  many 
other  considerations  arise  of  which  account  has  to  be  taken.  But 
the  general  principle  involved  is,  that  by  taking  a  sufficiently  large 
number  of  cases,  chance  can  be  almost  eliminated.  We  can  have 
no  means  of  determining  whether  any  healthy  individual  will  or 
will  not  die  before  the  end  of  the  year.  There  would  be  a  very 
serious  risk,  amounting  practically  to  gambling,  in  insuring  his 
life  alone,  for  probabilities  are  essentially  averages.  They  inform 
us  about  the  group,  and  not  directly  about  any  particular  mem- 
ber of  it.  But  the  transaction,  as  we  have  seen,  is  no  longer  a 
mere  speculation  when  a  large  number  of  individuals  are  con- 
cerned ;  for  the  actual  loss  can  be  accurately  foretold  and  pro- 
vided for. 

(2)  As  precise  an  analysis  of  the  conditions  as  is  possible  is  as 
important  in  estimating  probabilities  as  it  is  in  the  other  uses  of 
statistics.  The  smaller  the  group  of  which  the  average  is  taken, 
and  the  more  definite  the  information  we  have  about  it,  the  more 
accurate  our  estimate  becomes.  It  is  not  enough,  for  example, 
for  the  purposes  of  life-insurance,  to  know  what  the  average  age 
of  death  is,  all  adults  being  taken  as  on  the  same  footing.  What 
the  insurance  companies  do  is,  in  the  first  place,  to  exclude  all  who 
are  not  in  fairly  good  health,  and  who  may  be  in  danger  of  heredi- 
tary disease,  from  their  membership ;  and,  in  the  second  place,  to 
calculate  the  average  number  of  years  of  life  remaining  to  men  of 
different  ages.  Every  individual  is  thus  put  into  a  special  class, 
and  the  premium  calculated  accordingly. 

(3)  A  rather  common  fallacy  is  to  suppose  that  the  known  prob- 


232  Enumeration  and  Statistics 

ability  of  any  particular  event  of  a  group  or  series,  gives  us  somt 
ground  for  expecting  this  when  the  other  events  of  the  series  have 
occurred.  But  it  should  be  remembered  that  the  known  prob- 
ability affords  no  such  ground  of  inference,  except  as  we  know 
that  there  is  some  causal  relation  between  these  events;  and 
then  we  are  not  reasoning  by  probabilities.  The  probability  of 
throwing  double  six  with  two  dice,  for  example,  is  ^.  But  because 
in  35  consecutive  throws  the  double  six  has  not  appeared,  it  does 
not  follow  that  it  is  any  more  likely  to  do  so  on  the  36th  throw  than 
it  was  on  the  first.  The  probability  is  still  -^q,  and  so  continues. 
If  we  take  a  sufficiently  large  number  of  throws,  as  has  already 
been  remarked,  we  shall  find  that  the  double  six  has,  on  the  average, 
appeared  once  out  of  every  36  throws.  But  we  cannot  foresee 
whether  the  appearances  of  the  double  six  sufficient  to  give  this 
average  will  be  evenly  distributed  through  the  whole  series  of 
throws,  or  occur  in  irregular  sequences. 

(4)  A  peculiar  use  of  the  theory  of  probability  in  order  to  dis- 
cover causal  connections  between  events  is  possible  on  the  principle 
just  stated.  When  we  are  in  doubt,  that  is,  as  to  whether  two 
events  are  in  any  way  causally  connected,  we  can  by  collecting 
statistics  estimate  the  probability  of  their  appearing  together  on  the 
assumption  that  they  have  no  causal  relation.  Then  if  they  are 
found  to  appear  together  more  or  less  frequently  than  this  esti- 
mate, we  are  justified  in  assuming  that  there  is  some  causal  rela- 
tion between  them.  Suppose,  for  example,  we  are  studying  two 
characteristics  which  occasionally  appear  in  a  certain  species  of 
animal,  and  wish  to  determine  whether  they  have  any  essential 
connection.  We  find  on  examining  a  large  number  of  cases  that 
one  of  these  characteristics  appears  once  in  every  sixteen  individ- 
uals, on  the  average,  and  the  other  once  in  every  twenty.  If 
there  is  no  connection  between  them,  then,  on  the  theory  of 
probability,  the  chance  of  their  happening  together  is  3^.  But 
if  we  found  that  they  occurred  together  in  20  cases  out  of  every 


§  56.    The  Calculation  of  Chances  233 

100,  we  should  conclude  that  there  must  be  some  cause  or  cause.' 
common  to  both  characteristics,  or  else  that  one  of  them  in  some 
way  depends  on  the  other. 

REFERENCES 

C.  Sigwart,  Logic,  §§  101,  102. 

J.  G.  Hibben,  Inductive  Logic,  Ch.  XV. 

L.  T.  Hobhouse,  The  Theory  0}  Knowledge,  Pt.  II.,  Ch.  XI. 

J.  S.  Mill,  Logic,  Bk.  III.,  Ch.  XVIII. 

B.  Bosanquet,  Logic,  Vol.  I.,  pp.  128  ff. 


CHAPTER   XVI 

DETERMINATION    OF    CAUSAL    RELATIONS 

§  57.  Causal  Connection.  —  So  far,  we  have  been  dealing, 
primarily,  with  observational  methods,  and  with  the  results 
obtained  through  the  enumeration  of  particular  things.  We 
have  been  considering  how  our  knowledge  of  the  qualities 
and  quantities  of  objects  may  be  made  as  exact  and  com- 
plete as  possible,  but  we  have  not  discussed  in  detail  the 
methods  by  which  we  discover  the  connection  of  things. 
But  all  Inductive  thinking,  as  has  been  shown,  is  based 
on  the  assumption  that  there  are  universal  forms  or  prin- 
ciples of  relation  according  to  which  things  are  connected 
in  a  systematic  way.  We  cannot  really  be  said  to  know 
at  all,  until  we  become  aware  that  certain  parts  of  our 
experience  are  united,  like  the  links  of  a  chain,  one  part 
involving  another.  And,  as  has  been  already  frequently 
pointed  out,  the  growth  of  knowledge  is  constantly  bringing 
to  light  new  connections  between  facts  that  were  previously 
taken  to  be  independent  of  one  another.  Now,  it  was  also 
stated  in  an  earlier  chapter  (§51),  that  the  connections  and 
relations  of  things  may  be  conceived  in  different  ways — that 
there  are  various  '  categories  of  experience.'  Natural  science, 
however,  in  describing  and  explaining  the  relations  of  things, 
does  so  primarily  in  terms  of  Cause  and  Effect.  All  phenomena 
without  exception,  it  is  assumed,  are  causally  dependent  on 
other  phenomena;  everything  which  happens  has  its  cause, 
and  is  in  turn  followed  by  its  effect.     From  the  standpoint  of 

234 


§  57-    Causal  Co /meet  ion  235 

practical  experience,  also,  we  are  constantly  obliged  to  look 
for  causes ;  for  only  where  the  cause  is  known  is  there  any 
certain  method  of  producing  the  effect.  The  determination 
of  causes,  then,  is  one  of  the  most  essential  problems  of  Induc- 
tion, the  category  of  Cause  and  Effect  being  perhaps  the 
most  universal  and  important  category  by  means  of  which 
the  parts  of  our  experience  are  thought  as  related  according 
to  universal  laws.  What  rule,  or  rules,  can  now  be  given 
which  will  enable  one  to  discover  what  is  the  cause  or  the  effect 
of  an  event  in  any  particular  case  ? 

Before  we  proceed  to  the  answer  of  this  question,  however, 
it  is  necessary  to  explain  briefly  what  is  meant  in  the  natural 
sciences  by  the  relation  of  cause  and  effect.  In  the  first 
place,  the  natural  sciences  regard  the  world  as  consisting 
of  a  phenomenal  order  of  events.  In  other  words,  they 
are  concerned  with  the  particular  things  and  changing 
events  that  appear  or  show  themselves  in  ordinary  experi- 
ence. Both  the  inner  and  the  outer  world  appear  to  be 
composed  of  an  indefinite  manifoldness  of  particular  things, 
events,  occurrences.  Now,  the  natural  sciences  do  not  ask 
whether  this  aspect  of  the  world  is  ultimate  Reality  or  merely 
Appearance.  The  problem  of  the  scientist  is  rather  to  set 
out  from  the  manifold  objects  and  events  as  they  appear  in 
ordinary  experience,  and  to  seek  to  describe  and  explain  them 
by  showing  how  they  are  related  in  various  complex  ways 
through  principles  of  causal  dependence.  It  is  assumed 
that  each  phenomenon  of  which  the  world  is  composed,  is  yet, 
in  spite  of  the  independent  and  separate  existence  which  it 
seems  to  have,  connected  through  the  principle  of  causality 
with  something  else  which  determines  it,  or  is  in  some  way 
necessary  to  its  existence.     Every  event,  that  is,  has  its  cause. 


236  Determination  of  Causal  Relations 

^he  explanation  of  every  phenomenon  is  to  be  found  in 
something  external  to  it,  but  upon  which  it  is  dependent.  The 
relation  of  cause  and  effect  assumes  that  all  phenomena  are 
externally  determined ;  or,  as  the  same  thing  is  often  expressed, 
it  assumes  a  mechanical  relation  between  the  different  parts 
of  the  world.  Moreover,  this  relation  is,  as  has  been  said, 
simply  a  special  form,  or  category,  through  which  the  uni- 
versal relations  of  things  are  expressed.  That  there  are 
universal  modes  of  connection,  and  that  'once  true  always 
true,'  is  a  law  or  postulate  of  all  thinking.  Causality, 
being  as  we  have  seen  one  very  definite  and  useful  way  of 
thinking  that  relation,  is  accordingly  of  the  greatest  im- 
portance, both  for  science  and  practical  life. 

(1)  When  the  general  postulate  of  all  thinking,  that  things  shall 
hold  together  systematically  so  as  to  be  intelligible,  is  put  in  more 
definite  form  as  the  law  of  Cause  and  Effect  between  phenomena, 
we  get  the  notion  of  the  Uniformity  of  Nature.  Of  course,  strictly 
speaking,  the  Uniformity  of  Nature  is  involved  in  the  fundamental 
postulate  of  thought  that  things  hang  together  in  a  rational  way. 
Nevertheless,  the  conception  is  usually  taken  to  imply  the  absolutely 
invariable  sequence  of  causal  events.  From  the  point  of  view  of 
natural  science,  Nature  is  uniform  in  the  sense  that  all  instances  of 
the  same  phenomenon  P,  are  always  determined  in  the  same  way  by 
the  same  cause  Q.  This,  then,  is  really  mechanical  uniformity. 
The  relation  between  P  and  Q  is  not  only  external  or  mechanical, 
but  absolutely  fixed  and  invariable.  The  conception  of  any 
'spontaneous  variation,'  any  modification  without  an  externally 
determining  cause,  is  completely  excluded. 

(2)  In  speaking  of  any  phenomenon  as  having  a  cause,  the  relation 
has,  of  course,  been  artificially  simplified.  In  reality,  there  are 
always  a  number  of  '  causes,'  or  determining  conditions  necessary  to 


§  58.    Mill's  Experimental  Methods  23^ 

the  occurrence  of  any  event.  What  we  mean  by  'the  cause,'  in 
any  particular  case,  depends  mainly  on  the  character  and  purpose  of 
the  inquiry.  In  practical  life  the '  cause '  sought  for  is  usually  some- 
thing that  can  be  employed  directly  as  a  means  to  the  desired  result. 
And  even  in  scientific  inquiries  practical  motives  continue  to  play  a 
part  in  deciding  what  shall  be  regarded  as  the  '  essential '  or  '  real' 
cause  of  any  phenomenon.  The  cause  is  that  which  can  be  em- 
ployed to  produce  the  desired  effect,  and  so  to  afford  practical  mas- 
tery over  the  situation.  This  direct  reference  to  practice,  however, 
is  not  essential  to  the  idea,  which  is  primarily  a  way  of  thinking 
things  in  relation.  Ultimately,  then,  the  '  real'  or  'essential '  cause 
is  that  which  shows  most  clearly  the  character  of  the  relationship 
between  two  phenomena  —  that  which,  in  a  sense,  is  the  sum  or 
synthesis  of  all  the  conditions. 

The  cause,  then,  from  the  point  of  view  of  science,  is  that  with- 
out which  the  phenomenon  would  not  occur.  It  is  also  sometimes 
defined  as  'the  invariable  and  necessary  antecedent,'  while  the 
effect  is  spoken  of  as  the  'invariable  consequent.'  In  using  these 
terms,  however,  it  must  not  be  supposed  that  the  cause  always  and 
necessarily  precedes  the  effect  in  time.  The  relation  of  cause  and 
effect  is  not  to  be  regarded  as  merely  temporal. 

§  58.  Mill's  Experimental  Methods. — The  methods  by 
which  causes  and  effects  may  be  determined  were  formulated 
by  Mill  in  his  Logic.  He  stated,  in  general  terms,  the  prin- 
ciples which  were  already  in  use  in  scientific  procedure.  Mill 
gives  five  separate  canons,  but,  as  he  himself  recognizes, 
there  are  but  two  main  principles  involved.  "  The  simplest 
and  most  obvious  modes  of  singling  out  from  among  the 
circumstances  which  precede  or  follow  a  phenomenon,  those 
with  which  it  is  really  connected  by  an  invariable  law,  are 
two  in  number.  One  is,  by  comparing  together  different  in- 
stances in  which  the  phenomenon  occurs.    The  other  is,  by 


238  Determination  of  Causal  Relations 

comparing  instances  in  which  the  phenomenon  does  occur 
with  instances  in  other  respects  similar  in  which  it  does 
not.  These  two  methods  may  be  respectively  denominated 
the  Method  of  Agreement  and  the  Method  of  Differ- 
ence." 1  Of  the  other  three  methods  mentioned  by  Mill, 
one— the  Joint  Method  of  Agreement  and  Difference  —  is, 
as  the  name  implies,  a  direct  combination  of  the  first  two, 
while  the  Method  of  Residues  and  the  Method  of  Concomi- 
tant Variations  are  corollaries  from  the  same  principles. 

The  purpose  of  these  comparisons  is  to  exhibit  and  define 
the  true  cause.  This  is  accomplished  by  proceeding  directly 
through  negation.  That  is,  the  other  circumstances  which 
could  be  supposed  to  have  any  influence  are  successively 
eliminated.  And,  as  already  pointed  out  (§  50),  it  is  just  with 
a  view  to  the  possibility  of  elimination,  that  the  instances 
are  selected.  Since  the  cause  is  that  without  which  the  phe- 
nomenon would  not  occur,  the  rules  of  elimination  follow  im- 
mediately: (1)  That  is  not  the  cause  of  a  phenomenon  in 
the  absence  of  which  the  phenomenon  occurs;  (2)  That  is 
not  the  cause  of  a  phenomenon  in  whose  presence  the  phenom- 
enon fails  to  occur;  (3)  That  is  not  the  cause  of  a  phenome- 
non which  varies  when  it  is  constant,  or  is  constant  when  it 
varies,  or  varies  in  no  proportionate  manner  with  it.2 

The  process  of  eliminating  the  other  things  that  could 
conceivably  be  causes,  also  defines  the  sphere  and  nature  of  the 
true  cause.  The  preceding  rules,  then,  might  have  been 
stated  positively,  and  it  is  this  positive  side  of  the  process  that 

1  Mill,  Logic,  Bk.  III.,  Ch.  VIII.,  §  1. 

2  These  statements  are  essentially  those  given  by  Joseph  (An  Introduction 
to  Logic,  pp.  403-404),  who,  however,  adds  a  fourth  supplementary  rule: 
"Nothing  is  the  cause  of  one  phenomenon  which  is  known  to  be  the  cause 
pf  a  different  phenomenon." 


§  59-    The  Method  of  Agreement  239 

has  been  emphasized  by  Mill.  It  is  important  to  bear  in 
mind,  however,  in  studying  Mill's  Methods  of  Experimental 
Inquiry,  that  elimination  or  negation  plays  an  important 
part  in  the  process  which  he  describes.  We  shall  now  pro- 
ceed to  state  and  illustrate  the  canons  of  the  different  methods. 
§  59.  The  Method  of  Agreement.  —  The  principle  upon 
which  this  method  proceeds  is  stated  in  the  following  way 
by  Mill:  "  //  two  or  more  instances  of  the  phenomenon  under 
investigation  have  only  one  circumstance  in  common,  the 
circumstance  in  which  alone  all  the  instances  agree  is  the  cause 
{or  effect)  of  the  given  phenomenon."  The  purpose  of  this 
rule,  it  will  be  remembered,  is  to  help  us  to  determine  what 
particular  facts  in  our  experience  are  connected  as  causes  and 
effects.  If  the  problem  is  to  find  the  cause  of  some  phenome- 
non, the  canon  may  be  illustrated  in  the  following  way.  Let 
P1,  P2,  P3,  represent  different  instances  of  a  phenomenon, 
P,  whose  cause  is  to  be  ascertained.  And  suppose  that  we  are 
able  to  analyze, 

the  antecedents  of  P1  into  abed; 

the  antecedents  of  P2  into  gfcm; 

the  antecedents  of  P3  into  klnc. 

Now  it  is  clear  that  c  is  the  sole  circumstance  in  which  the 
antecedents  of  all  these  instances  of  P  agree.  And  nothing 
can  be  the  cause  of  P  in  the  absence  of  which  P  still  occurs. 
We  should  be  justified  in  concluding,  therefore,  according  to 
this  method,  that  c  is  probably  the  cause  of  the  phenomenon 
under  investigation,  P.  We  may,  then,  adopt  Jevons's 
formula  for  discovering  the  cause  of  any  given  phenomenon  by 
this  method :  '  The  sole  invariable  antecedent  of  a  phenomenon 
is  probably  its  cause? 


'4-0  Determination  of  Causal  Relations 

If,  now,  we  wished  to  discover  the  effect  of  something  which 
happens,  it  would  be  necessary  to  determine,  by  observing 
a  number  of  instances,  what  common  circumstance  can  be 
found  among  the  events  which  follow  it. 

If  Q1  were  followed  by  fghk, 
and  Q2  were  followed  by  hngc, 
and  Q3  were  followed  by  grst, 

we  should  be  able  to  say  that  Q  and  g  were  connected  as  cause 
and  effect.  The  rule  might  then  be  expressed:  The  sole 
invariable  consequent  of  a  phenomenon  is  probably  its  effect. 

When  antecedents  and  consequents  are  thus  represented 
schematically  by  means  of  letters,  it  is  easy  to  perceive  at 
once  the  common  circumstance  in  a  number  of  instances. 
But  the  facts  and  events  of  the  real  world  are  not  separated 
off  from  each  other  in  this  way.  The  common  circumstance 
in  which  a  number  of  instances  agree  has  to  be  separated  out 
by  analysis  from  the  variable  elements  which  form  part  of  the 
different  antecedents  and  consequents.  Moreover,  an  essen- 
tial part  of  the  work  of  Induction  consists  in  selecting  in- 
stances such  that  all  the  possibilities — all  the  things  that  might 
be  connected  with  P — are  included.  It  should  also  enable 
us  to  recognize  the  common  element  as  common,  though  it 
may  appear  in  wholly  different  circumstances.  The  way  in 
which  the  work  of  analysis  proceeds  will  become  more  evident 
by  considering  a  number  of  concrete  cases  in  which  this 
method  may  be  employed. 

If  a  number  of  cases  of  typhoid  fever  were  to  appear  at 
about  the  same  time  in  a  community,  one  would  naturally 
wish  to  explain  this  phenomenon  by  tracing  it  to  its  cause; 
and  to  do  this  one  would  try  to  discover  some  circumstance 


§  59-    The  Method  of  Agreement  241 

which  was  the  common  antecedent  of  all  the  cases.  Knowing 
from  the  records  of  past  experience  that  the  cause  is  to  be 
sought  for  among  a  limited  number  of  circumstances,  one 
would  select  the  various  instances  with  the  purpose  of  testing 
the  different  possibilities.  The  water  supply  might  first  be 
examined.  But  if  it  were  found  that  this  was  derived  from 
entirely  different  sources  in  the  different  cases,  we  should 
probably  conclude  that  the  explanation  must  be  sought  else- 
where. Suppose  that  as  a  result  of  careful  analysis  it  were 
discovered  that  all  the  individuals  prostrated  with  the  fever 
had  eaten  oysters  bought  at  the  same  market.  If  this  were  the 
only  common  circumstance  discoverable  after  careful  investi- 
gation, we  should  conclude  that  probably  the  oysters  were  the 
cause  of  the  fever.  The  process  of  analysis  could  be  pushed 
still  further,  if  one  wished,  in  order  to  determine  more  exactly 
the  precise  source  of  the  infection:  e.g.  it  might  be  found,  as  a 
result  of  further  inquiry,  that  the  water  in  which  the  oysters 
were  kept  was  vitiated  by  a  sewer. 

Another  example  of  the  method  of  agreement  which  is 
often  quoted  by  logicians  may  be  given.  One  would  natu- 
rally suppose  that  the  colours  and  lines  of  mother-of-pearl 
were  due  to  the  chemical  or  physical  character  of  the  sub- 
stance itself.  Sir  David  Brewster,  however,  happened  to 
take  an  impression  of  a  piece  of  mother-of-pearl  in  beeswax 
and  resin,  and  was  surprised  to  see  the  colours  reproduced 
upon  its  surface.  He  then  took  a  number  of  other  impressions 
in  balsam,  gum-arabic,  lead,  etc.,  and  found  the  iridescent 
colours  repeated  in  every  case.  In  this  way  he  proved  that 
the  colours  were  caused  by  the  form  of  the  substance,  and  not 
by  its  chemical  qualities  or  physical  composition.  The  differ- 
ent substances,  wax,  balsam,  lead,  etc.,  in  which  the  phenome 

R 


242  Determination  of  Causal  Relations 

non  of  colour  appeared,  had  nothing  in  common  except  the 
form.  This,  therefore,  according  to  the  method  of  agreement, 
was  properly  regarded  as  the  cause  of  the  phenomenon  to  be 
explained. 

An  example  of  the  application  of  this  method  to  the  discovery 
of  the  effect  of  a  phenomenon  may  now  be  given.  Let  us 
suppose  that  the  problem  is  to  determine  the  effect  of  some 
proposed  legislation.  It  is  necessary,  of  course,  to  refer  to 
other  instances  where  this  legislation  has  been  put  in  force, 
and  our  general  information  about  political  and  social  affairs 
shows  more  or  less  definitely  what  kind  of  connected  circum- 
stances it  is  worth  while  noting.  Let  us  suppose  that  in  one 
case  what  followed  the  enactment  of  the  law  under  considera- 
tion was  a  falling  off  of  revenue,  an  increase  of  immigration, 
large  exports,  etc.,  and  in  a  second,  the  revival  of  ship-building, 
decrease  of  crime,  and  increase  of  immigration;  and  that  in 
other  instances  where  still  other  conditions  prevailed,  the 
number  of  immigrants  still  continued  to  increase.  Since  this 
latter  circumstance  is  the  only  one  which  follows  invariably 
upon  the  enactment  of  the  law,  we  are  justified  in  concluding, 
after  a  certain  number  of  observations,  that  it  is  necessarily 
connected  with  the  law  as  its  result. 

It  is  important  to  note  that  the  conclusions  reached  by  this 
method  are  greatly  strengthened  by  increasing  the  number  of 
observations,  and  by  taking  as  many  instances  as  possible 
that  are  dissimilar  in  character.  By  so  doing,  the  real 
cause  is  more  likely  to  be  included  among  the  antecedents 
noted,  and,  at  the  same  time,  the  probability  is  lessened  that 
the  connection  between  antecedent  and  consequent  is  a 
merely  accidental  conjunction.  But  even  when  such  pre- 
cautions are  taken,  the  method  of  Agreement  does  not  afford 


§  59-    The  Method  of  Agreement  243 

any  very  definite  knowledge.  By  eliminating  the  other  ante- 
cedents, we  found  that  c  is  probably  connected  causally  with 
P.  But  c  is  left  as  a  mere  unanalyzed  '  circumstance,'  e.g. 
'  the  drinking  water,'  '  the  form '  of  the  substances  which 
showed  iridescent  colours,  etc.  Just  how  the  connection  takes 
place,  whether  it  be  direct  or  indirect,  is  not  shown.  It  is 
clear;  then,  that  further  analysis  is  necessary  in  the  interest  of 
scientific  knowledge.  The  method  of  Agreement,  although 
perhaps  in  some  cases  yielding  results  sufficiently  exact  for 
practical  application,  merely  suggests  a  problem  for  further 
scientific  inquiry.  Its  defect,  as  we  have  seen,  is  that  it  does 
not  sufficiently  get  beneath  the  surface  of  things  so  as  to  make 
certain  and  definite  their  mode  of  relation. 

It  may  be  well  to  notice  under  separate  headings  some  of  the 
special  difficulties  which  result  from  this  method's  superficial  mode 
of  analysis. 

(1)  Reciprocity  of  Phenomena.  So  long  as  we  are  dealing  with 
events  which  succeed  one  another  in  time,  there  is  no  difficulty  in 
perceiving  which  is  cause,  and  which  effect.  But  we  are  often 
called  upon  to  investigate  the  relation  between  phenomena  that 
do  not  appear  as  successive,  but  as  co-existent.  And  it  is  then  not 
at  all  easy  to  determine  by  means  of  the  method  of  Agreement 
which  is  cause  and  which  is  effect.  Poverty  and  intemperance,  for 
example,  are  found  conjoined  so  frequently  as  to  make  it  probable, 
apart  from  other  considerations,  that  some  causal  relation  exists 
between  them.  It  might  be  maintained  with  apparently  equal 
show  cf  reason,  that  the  former  is  the  cause,  or  the  effect,  of  the 
latter.  Again,  is  one  to  say  that  ignorance  is  the  cause  or  the  effect 
of  moral  degradation  ?  There  seems  to  be  no  means  of  determin- 
ing by  this  method  which  is  antecedent  and  which  consequent. 
As  a  matter  of  fact,  it  is  probably  true  in  such  cases  that  the  phe- 
nomena act  and  react  upon  each  other :  that  each  term,  in  other 


244  Determination  of  Causal  Relations 

words,  is  at  once  both  cause  and  effect.  In  such  instances  we  gc 
beyond  the  conception  of  causal  dependence  in  one  direction,  to  that 
of  the  Reciprocity  of  phenomena. 

(2)  Complexity  of  Phenomena.  Again,  neither  the  cause  nor  the 
effect  need  be  composed  of  a  single  phenomenon,  as  the  method 
seems  to  assume.  Indeed,  as  further  observation  shows,  the  ante- 
cedents and  consequents  which  the  method  of  Agreement  takes  as 
'single  circumstances'  are  usually  very  complex.  The  difficulty  is 
that  the  process  of  analysis  has  not  been  carried  far  enough  to  bring 
out  the  essential  point  involved.  Everything  is  lumped  together 
and  the  exact  nature  of  the  connection  left  vague  and  uncertain. 
Thus,  for  example,  the  '  ill-health '  of  a  community  might  be  shown 
by  this  method  to  be  related  causally  to  the  'sanitary  conditions.' 
Here  it  is  obvious  that  both  antecedent  and  consequent  involve  com- 
plex relations  and  conditions,  which  are  left  vague  and  ill-defined. 

(3)  Plurality  of  Causes.  There  is  still  another  circumstance  that 
renders  uncertain  the  results  of  the  method  of  Agreement.  In 
itself,  it  can  only  show  that  c  is  a  cause  of  P,  not  that  it  is  the  only 
or  necessary  cause.  Taking  the  word  '  cause '  in  its  popular  sense, 
we  cannot  say  that  a  given  phenomenon  is  always  produced  by 
the  same  cause,  or  that  the  effects  of  different  causes  are  always 
different.  Intemperance  may  result  from  different  causes  in 
different  cases,  or  heat  may  be  generated  through  combustion, 
friction,  or  electricity.  The  fact  here  illustrated,  that  an  effect 
may  be  produced  by  any  one  of  several  causes,  is  what  is  meant  by 
the  phrase  'Plurality  of  Causes.'  Once  more,  this  defect  is 
simply  the  result  of  a  too  vague  or  superficial  analysis.  When 
analysis  can  discover  what  has  really  occurred,  what  the  real  nature 
of  the  effect  is,  it  becomes  possible  to  determine  the  nature  of  the 
only  and  essential  cause. 

§  60.  The  Method  of  Difference.  —  According  to  the 
method  of  Agreement,  we  compare  a  number  of  diverse  in- 
stances, in  all  of  which  a  given  phenomenon  occurs,  and  en- 


§  60.    The  Method  of  Difference  245 

deavour  to  discover  the  one  circumstance  which  is  invariably 
present.    The  method  of  Difference,  on  the  other  hand,  com- 
pares an  instance  in  which  a  phenomenon  occurs  with  another 
as  nearly  similar  to  it  as  possible,  in  which  it  does  not  occur. 
Its  canon  is  expressed  by  Mill  as  follows:  "If  an  instance 
in  which  the  phenomenon  under  investigation  occurs,  and  an 
instance  in  which  it  does  not  occur,  have  every  circumstance  in 
common  save  one,  that  one  occurring  only  in  the  former;   the 
circumstance  in  which  alone  the  two  instances  differ  is  the  effect, 
or  the   cause,  or  an  indispensable  part  of  the  cause,  of  the 
phenomenon"    It  will  perhaps  make  the  matter  clearer  to  say: 
'That  which  is  present  in  a  case  when  a  phenomenon  occurs, 
and  absent  in  another  case  when  that  phenomenon  does  not 
occur,  all  other  circumstances  remaining  the  same  in  the  two 
cases,  is  causally  connected  with  that  phenomenon.'    That  is, 
by  means  of  this  method  we  compare  two  instances  which 
differ  only  in  the  fact  that  the  phenomenon  in  which  we  are 
interested,  is  present  in   the  one,  and  absent   in   the  other. 
If  now  the  two  cases  are  represented  in  this  way, 
PHK  conjoined  with  alg, 
and  HK  conjoined  with  Ig, 
we  conclude  at  once  that  P  is  causally  connected  with  a.    Our 
selection  of  P,  or  the  element  in  question,   as  the  supposed 
cause,  is,  of  course,  made  in  accordance  with  an  hypothesis  or 
general  notion  of  what  the  possible  or  likely  causal  relations 
in  the  subject  under  investigation  are,  gathered  from  previous 
experience.     If  this  notion  is  as  yet  too  vague  to  give  us  any 
definite  guidance,  then  we  are  obliged  to  analyze  the  phenom- 
ena as  exactly  and  minutely  as  we  can,  and  experimentally 
vary  the  circumstances  in  every  conceivable  way,  until  the 
requirements  of  the  method  are,  if  possible,  satisfied. 


246  Determination  of  Causal  Relations 

Almost  any  instance  in  which  experiment  is  employed  wih 
serve  to  illustrate  this  method.  If  a  bell  is  rung  in  a  jaf 
containing  air,  the  sound  will,  of  course,  be  heard  at  any  ordi- 
nary distance.  But  after  having  removed  the  air  by  means  of 
an  air-pump,  let  the  bell  be  again  struck.  It  will  now  be 
found  that  the  sound  is  no  longer  heard.  When  the  two  cases 
are  compared,  it  is  at  once  evident  that  the  only  difference  in 
the  antecedents  is  the  presence  of  the  air  in  the  one  case,  and 
its  absence  in  the  other.  When  the  air  was  present,  the 
sound  was  heard;  when  it  was  absent,  the  sound  was  not  heard. 
We  conclude,  therefore,  that  the  perception  of  sound  is  caus- 
ally connected  with  the  presence  of  atmospheric  air.  Again, 
we  can  prove  that  the  so-called  'taste'  of  different  objects 
depends  upon  smell,  by  tasting,  say,  an  orange,  and  after  a 
little  time  has  elapsed,  tasting  it  a  second  time  while  holding 
the  nose.  It  will  be  found  in  this  latter  case  that  instead  of 
the  familiar '  orange  taste,'  one  senses  merely '  acid,'  or '  sweet.' 
The  only  difference  in  the  two  trials  being  that  in  the  former 
the  organ  of  smell,  which  was  excluded  in  the  latter,  was  oper- 
ative, it  follows  that  the  so-called  'orange  taste'  is  proved 
to  be  due  to  smell  rather  than  to  taste  proper. 

An  essential  requirement  of  the  method  of  Difference  is 
that  only  one  circumstance  shall  be  varied  at  a  time.  The 
object  of  the  method  is  to  isolate  the  various  conditions  which 
go  to  make  up  a  complex  phenomenon,  in  order  that  we  may 
mark  the  effect  of  the  presence  or  absence  of  each  one  individ- 
ually. Now,  in  observing  what  goes  on  in  nature,  we  rarely 
find  changes  in  which  but  a  single  element  has  varied.  If 
we  find  that  to-day  is  cooler  than  yesterday,  we  may  be  in- 
clined to  refer  the  change  to  the  thunder-storm  of  last  night. 
But  rain  also  accompanied  the  thunder-storm,  and  the  direc- 


§  6o.    The  Method  of  Difference  24; 

tion  of  the  wind  has  changed.  So  that  it  is  impossible  in 
such  cases  to  apply  the  method  of  difference.  To  employ  this 
method  successfully,  observation  usually  must  be  supple- 
mented by  experiment.  In  performing  experiments,  we 
determine  what  conditions  are  to  be  operative,  and  arrange 
the  apparatus  so  as  to  carry  out  our  purpose.  Having  thus 
control  of  the  conditions,  we  are  able  to  vary  them  at  pleasure. 
In  this  way,  experiment  becomes  an  instrument  by  means  of 
which  analysis  can  be  carried  further  than  is  possible  for  un- 
aided observation.  It  enables  us  to  separate  things  which  are 
usually  conjoined,  and  to  observe  the  result  of  each  when 
taken  by  itself.  In  employing  experiment,  however,  the 
greatest  care  must  always  be  taken  to  introduce  or  remove 
only  one  condition  at  a  time,  or  at  least  only  one  new  circum- 
stance which  can  in  any  way  influence  the  result. 

It  often  happens,  too,  as  Jevons  points  out,  that  the  ex- 
perimenter is  not  aware  of  all  the  conditions  which  are  opera- 
tive when  his  investigations  are  made.  '  Some  substance 
may  be  present,  or  some  power  may  be  in  action  which  escapes 
the  most  vigilant  examination.  Not  being  aware  of  its 
existence,  we  are  of  course  unable  to  take  proper  measures  to 
exclude  it,  and  thus  determine  the  share  which  it  may  have 
in  the  results  of  our  experiments.' *  For  this  reason,  it  is 
always  necessary  that  experiments  should  be  repeated  by 
different  persons,  and  so  far  as  possible  under  varying  condi- 
tions. I  quote  two  examples  from  the  work  of  Jevons  to 
which  reference  has  just  been  made. 

"  One  of  the  most  extraordinary  instances  of  an  erroneous  opin- 
ion due  to  overlooking  interfering  agents  is  that  concerning  the 
increase  of  rainfall  near  the  earth's  surface.     More  than  a  century 

1  Jevons,  Principles  of  Science,  Vol.  II.,  p.  37. 


248  Determination  of  Causal  Relations 

ago  it  was  observed  that  rain  gauges  placed  upon  church  steeples, 
house-tops,  and  other  elevated  places,  gave  considerably  less  rain 
than  if  they  were  on  the  ground,  and  it  has  very  recently  been 
shown  that  the  variation  is  most  rapid  in  the  close  neighbourhood 
of  the  ground.  All  kinds  of  theories  have  been  started  to  explain 
this  phenomenon ;  but  I  have  attempted  to  show  that  it  is  simply 
due  to  the  interference  of  wind  which  deflects  more  or  less  rain 
from  all  the  gauges  which  are  at  all  exposed  to  it. 

"  The  great  magnetic  power  of  iron  renders  it  a  constant 
source  of  disturbance  in  all  magnetic  experiments.  ...  In 
some  cases,  magnetic  observations  have  been  seriously  disturbed 
by  the  existence  of  masses  of  iron  in  the  neighbourhood.  In 
Faraday's  experiments  upon  feebly  magnetic  or  diamagnetic 
substances,  he  took  the  greatest  precautions  against  the  presence 
of  any  disturbing  substance  in  the  copper  wire,  wax,  paper,  and 
other  articles  used  in  suspending  the  test  objects.  It  was  his  in- 
variable custom  to  try  the  effect  of  the  magnet  upon  the  appara- 
tus in  the  absence  of  the  object  of  experiment,  and  without  this 
preliminary  trial  no  confidence  could  be  placed  in  the  results."1 

It  is  sometimes  impossible  to  remove  the  suspected  cause 
experimentally  without  materially  changing  the  attendant 
circumstances;  or  it  may  be  impossible  to  remove  it  at  all, as  in 
the  case  of  gravity.  But  this  difficulty  may  often  be  over- 
come by  introducing  a  circumstance  which  overcomes  or 
neutralizes  the  effect  of  the  supposed  cause  without  altering  the 
rest  of  the  phenomena.  Thus,  e.g.,  the  rain  gauges  placed  in 
elevated  positions  which  were  mentioned  above,  might  be 
protected  from  the  wind  by  screening.  The  effect  of  this 
disturbing  element  would  thus  be  neutralized,  leaving  it 
possible  to  observe  what  results,  if  any,  in  the  quantity  of 
rainfall  followed  a  change  of  elevation. 

1Jcvons,  op.  oil.,  pp.  40,  41. 


CHAPTER    XVII 

DETERMINATION   OF   CAUSAL   RELATIONS    (continued) 

§  61.   The  Joint  Method  of  Agreement  and  Difference.  — 

The  method  of  Difference  can  be  applied  only  when  all 
concomitant  circumstances,  except  one,  remain  constant.  In 
order  to  apply  this  method,  then,  it  is  necessary  either  to 
find  two  instances  which  differ  only  in  a  single  circumstance, 
or  to  proceed  by  means  of  experiments,  adding  or  removing 
a  single  circumstance  at  a  time  and  noting  the  result.  The 
difficulty  is  to  find  instances  that  differ  only  in  a  single 
circumstance  in  fields  where,  from  the  nature  of  the  case, 
experiments  cannot  be  used.  For  example,  in  trying  to 
reach  generalizations  regarding  the  behaviour  of  human 
individuals  or  human  societies  — in  looking  for  moral,  or  so- 
cial, or  economic  laws  —  it  is,  of  course,  impossible  to  em- 
ploy experiment.  Nor,  when  dealing  with  individuals  and 
societies,  can  we  find  two  instances  which  certainly  differ 
from  each  other  in  only  a  single  circumstance.  In  studying 
phenomena  of  this  kind,  then,  it  is  necessary  to  employ  an- 
other method  as  an  instrument  cf  analysis.  What  is  done 
by  this  new  method  is  to  take  a  number  of  instances  instead 
of  only  two.  A  number  of  instances  where  the  phenomenon 
to  be  investigated  occurs  are  compared  together,  and  like- 
wise a  number  of  instances  where  it  does  not  occur,  and 
the  results  of  the  two  comparisons  noted. 

This  is  really  to  combine  theprinciple  of  themethod  of  Agree- 
ment with  that  of  the  method  of  Difference.  Mill,  accordingly, 

249 


250  Determination  of  Causal  Relations 

has  called  this  the  Joint  Method  of  Agreement  and  D\i 
ference,  and  has  given  the  following  statement  of  its  canon:— 
"  If  two  or  more  instances  in  which  the  phenomenon  occurs  have 
only  one  circumstance  in  common,  while  two  or  more  instances  in 
which  it  does  not  occur  have  nothing  in  common  save  the  absence 
of  that  circumstance,  the  circumstance  in  which  alone  the  two 
sets  of  instances  differ  is  the  effect,  or  the  cause,  or  an  indis- 
pensable part  of  the  cause,  of  the  phenomenon.'1''  By  the  help 
of  this  method,  the  weakness  which  has  already  been  noticed 
in  the  method  of  Agreement  is  overcome.  We  first  compare 
different  instances  in  which  the  phenomenon  occurs.  If 
these  are  found  to  agree  in  only  a  single  circumstance,  we 
conclude,  according  to  the  canon  of  Agreement,  that  this  cir- 
cumstance is  probably  connected  causally  with  the  phe- 
nomenon in  which  we  are  interested.  But  the  proof  is  not 
yet  complete.  To  really  prove  the  connection,  we  must 
show  that  wherever  the  circumstance  is  absent,  there  the 
phenomenon  is  also  absent. 

In  interpreting  this  canon,  it  is  important  to  remember 
that  both  positive  and  negative  instances  must  be  selected 
from  the  field  within  which  our  previous  knowledge  enables 
us  to  say  that  the  cause  (or  effect)  sought  for  is  to  be  found. 
The  purpose  of  the  instances,  as  has  been  frequently  pointed 
out,  is  to  bring  to  our  attention  circumstances  which  might 
conceivably  make  a  difference.  It  is,  of  course,  impossible 
to  predict  in  advance  all  the  things  that  might  make  a  differ- 
ence; but  the  possibilities  fall  within  a  more  or  less  definite 
range.  In  both  the  positive  and  negative  set  of  instances, 
then,  we  are  concerned  only  with  circumstances  that  might 
be  relevant.  The  negative  instances  to  be  chosen  are  there- 
fore, not  any  cases  '  where  the  phenomenon  does  not  appear,' 


§  6i.  Joint  Method  of  Agreement  and  Difference      251 

but  where,  in  addition,  circumstances  which  were  previously 
found  in  conjunction  with  the  phenomenon,  and  which  might 
have  been  supposed  to  be  causally  connected  with  it,  are  now 
shown  to  be  sometimes,  at  least,  present  when  it  is  absent. 
To  represent  the  working  of  the  matter  schematically,  we 
may  analyze  the  instances  where  the  phenomenon,  P,  occurs 
into  the  following  circumstances :  — 

Instance  1 a,  b,  c,  d,  e. 

Instance  2 f,  c,  a,  g,  k. 

Instance  3 d,  m,  b,  c,  e. 

Instance  4 k,  n,  c,  g,  a. 

The  method  of  Agreement,  in  such  a  case,  would  lead  to  the 
conclusion  that  c  is  probably  connected  causally  with  P. 
To  strengthen  and  render  more  definite  that  conclusion, 
however,  the  Joint  method  introduces  the  comparison  of 
instances,  as  much  like  the  former  group  as  possible  and 
known  to  exhibit  at  least  many  of  the  same  circumstances, 
but  where  the  phenomenon  in  question  does  not  occur.  These 
instances  of  the  absence  of  P  would  then  be  represented 
thus:  — 

Instance  1 b,  k,  n,  g,  a. 

Instance  2 d,  e,  b,  m,  f. 

Instance  3 k,  I,  s,  g,  b. 

Instance  4 x,  e,  n,  a,  f. 

What  is  of  significance  in  this  latter  series  is  not  merely  that 
the  instances  show  nothing  common  except  the  absence  of  P, 
but  that  the  same  '  circumstances  '  excluded  by  the  former 
analysis  are  now  seen  to  exist  in  the  absence  of  that  phenom- 
enon. But  what  may  be  present  when  a  phenomenon  is 
absent  is  not  its  cause  or  effect.     All  these  possible  circum- 


252  Determination  of  Causal  Relations 

stances,  then,  a,  b,  d,  etc.,  are  again  eliminated  by  the  com 
parison  of  negative  instances,  leaving  as  before  c  as  that 
which  is  causally  connected  with  P. 

The  canon  of  this  method,  then,  as  stated  by  Mill  must  be 
read  with  these  restrictions  in  mind.  The  actual  working  of 
the  method  is  better  described  in  the  following  words: 
If  when  two  sets  of  instances — one  in  which  the  phenome- 
non under  investigation  is  present  and  one  in  which  it  is 
absent  —  are  drawn  from  the  same  field  of  inquiry,  it  is  found 
that  there  is  one  circumstance  which  is  invariably  present 
when  the  phenomenon  occurs  and  invariably  absent  when  it 
does  not  occur,  while  each  of  the  other  circumstances  is  both 
sometimes  absent  when  the  phenomenon  is  present,  and  some- 
times present  when  it  is  absent,  then  the  first  circumstance  is 
causally  connected  with  the  phenomenon. 

As  an  illustration  of  the  method  of  Agreement  and  Difference 
the  following  instance  will  serve:  — 

We  may  suppose  that  in  a  certain  part  of  the  country  it 
was  noticed  that  a  considerable  difference  existed  in  the 
number  of  criminal  offences  committed,  in  proportion  to 
the  number  of  inhabitants,  in  the  various  towns.  In  several 
towns  the  percentage  was  high,  while  in  others  it  was  rela- 
tively small.  This  being  so,  a  question  naturally  arose  as 
to  the  cause  of  the  high  percentage.  Now  there  were  among 
the  people  various  opinions  concerning  the  matter.  One 
thought  it  was  due  to  the  small  number  of  police,  a  second 
believed  it  was  caused  by  the  inefficiency  of  the  public 
schools,  a  third  attributed  it  to  the  inadequacy  of  the  penal- 
ties attached  to  the  violation  of  law,  a  fourth  was  convinced 
that  it  was  due  to  lack  of  activity  on  the  part  of  the  churches, 
while  a  fifth  insisted  that  the  phenomenon  could  be  accounted 


§  6i.  Joint  Method  of  Agreement  and  Difference     253 

for  by  the  presence  of  licensed  saloons.  Not  being  able  to 
agree  about  the  matter,  it  was  decided  to  appoint  a  commit- 
tee to  investigate  the  circumstances  existing  in  various  towns 
where  the  same  general  conditions  prevailed,  and  upon  the 
basis  of  this  comparison  to  decide  the  matter.  The  towns 
with  a  high  criminal  percentage  were  examined  first.  The 
report  of  conditions  there  was  as  follows:  — 

Town   A:     Small    police    force — efficient   schools — severe 

penalties  — inactive  churches  — licensed  saloons. 
Town    B :     Small    police    force  —  efficient    schools  —  light 

penalties — active    churches — licensed  saloons. 
Town  C :   Large  police  force  —  inefficient  schools  —  severe 

penalties — active    churches — licensed   saloons. 
Town  D :  Large    police    force  —  inefficient    schools  —  light 

penalties — inactive     churches — licensed  saloons. 

This  report  revealed  the  fact  that  in  each  of  these  towns 
having  a  high  criminal  percentage  there  was  one  circumstance, 
and  only  one,  invariably  present,  —  the  licensed  saloon.  This 
rendered  it  probable  that  the  saloon  was  the  cause  of  the  high 
percentage  of  crime.  Still,  before  finally  deciding,  it  was 
thought  well  to  investigate  negative  instances  as  well;  that  is, 
towns  in  which  the  high  percentage  of  crime  did  not  occur. 
The  report  of  conditions  there  was  as  follows:  — 

Town  E :  Large  police  force  —  efficient  schools  —  severe 
penalties  —  active  churches — no  licensed  saloons. 

Town  F:  Large  police  force — inefficient  schools — light 
penalties — active  churches — no  licensed  saloons. 

Town  G :  Small  police  force  —  efficient  schools  —  light 
penalties — inactive  churches — no  licensed  saloons. 


254  Determination  of  Causal  Relations 

Town  H :  Small  police  force  —  inefficient  schools  —  severe 
penalties — active  churches — no  licensed  saloons. 

This  table  showed  that  in  the  absence  of  the  phenomenon 
(high  criminal  percentage)  one  and  only  one  of  the  condi- 
tions concerned  was  invariably  absent ;  namely,  the  licensed 
saloon.  This  confirmed  the  previous  report  and  established 
to  the  satisfaction  of  all  that  the  saloon  was,  at  least,  the 
main  cause  of  the  high  criminal  percentage  in  the  cities 
concerned. 

Of  course,  it  is  obvious  that  this  can  be  no  more  than  a  hypothet- 
ical case.  In  actual  life,  the  conditions  of  the  method  would  never 
be  so  exactly  realized.  In  the  first  place,  in  any  such  investigation, 
it  would  probably  never  be  possible  to  find  instances  where  one  con- 
dition is  invariably  present  when  the  phenomenon  occurs,  and 
invariably  absent  when  it  does  not  occur,  as  the  illustration  supposes. 
We  could,  at  most,  expect  that  one  condition  would  exhibit  a 
tendency  to  be  present  when  the  phenomenon  occurs  and  absent 
when  it  does  not  occur.  That  is,  there  might  well  be  instances 
met  with  in  which  a  combination  of  other  conditions  might  render 
unnecessary  the  presence  of  the  usually  essential  one.  In  the 
second  place,  it  would  not  be  satisfactory  in  actual  life  to  deal  with 
such  vague  terms  as  'efficient'  schools,  or  'active'  churches.  On 
the  contrary,  we  should,  in  a  careful  investigation,  resort  to  statistics 
in  order  to  secure  greater  definiteness  and  accuracy.  The  compar- 
ative number  of  the  churches,  the  'size  of  the  police  force,  the 
number  of  saloons,  would  be  noted  and  compared  with  the  per- 
centage of  crime  in  order  if  possible  to  determine  which  of  the 
above-mentioned  circumstances  is  causally  connected  with  the 
large  number  of  criminals.  That  is,  although  we  should  not  be 
likely  to  find  fulfilled  the  strict  requirements  which  this  method 
makes,   we  should  strengthen   the   inference   by   showing  that 


§  62.    The  Method  of  Concomitant   Variations         255 

definite  quantitative  relations  exist,  as  indicated  by  the  statistics, 
between  certain  of  the  circumstances  in  question. 

It  is  usual  to  speak  of  this  method  as  that  to  which  recourse 
must  be  had  when  it  is  impossible  to  employ  experiment.  As  a 
matter  of  fact,  this  illustration  seems  to  show  that  the  strict  require- 
ments of  the  method  can  never  be  realized  except  where  experi- 
ment can  be  employed  to  isolate  and  control  the  conditions.  In 
fields  where  this  is  impossible,  it  is  necessary,  as  we  have  seen,  to 
employ  statistics  as  an  instrument  of  analysis.  Where  the  method 
is  not  supplemented  by  determining  the  relation  of  the  various  in- 
stances experimentally,  or  by  making  possible  exact  comparisons 
through  the  use  of  statistics,  it  can  yield  only  vague  and  unsatis- 
factory results.  It  is  obvious,  therefore,  that  the  various  methods 
must  continually  supplement  one  another  in  actual  operation  if  the 
complex  and  changing  conditions  of  experience  are  to  be  success- 
fully dealt  with  at  all. 

§  62.  The  Method  of  Concomitant  Variations.  —  The 
methods  of  Agreement  and  Difference  are  employed,  as  we 
have  seen,  to  determine  what  events  are  necessarily  con- 
nected as  causes  and  effects.  By  examining  a  considerable 
number  of  instances,  and  by  comparing  the  cases  in  which 
the  phenomenon  of  interest  to  us  occurs,  with  cases  in  which 
it  does  not  occur,  we  seek  to  rule  out  all  accidental  and  un- 
essential conjunctions,  and  thus  to  determine  the  true  law 
of  causal  connection.  But  the  discovery  of  certain  forms  of 
agreement  or  correspondence  in  the  variations  of  phenomena, 
or  groups  of  phenomena,  often  enables  us  to  detect  a  causal 
relation  between  them  (cf.  pp.  222-224).  The  variations  or 
changing  states  of  all  phenomena  are  events  in  time.  Now, 
when  it  is  observed  that  certain  of  these  events  continue  to 
show  correspondences  throughout  a  series  of  variations,  it 
is  inferred  that  the  conjunction  is  not  accidental,  but  indi- 


256  Determination  of  Causal  Relations 

cates  the  existence  of  a  causal  connection.  This  correla- 
tion of  events  may  be  discovered  through  correspondences 
in  temporal  or  spatial  arrangement  of  phenomena,  in  their 
progression,  or  in  changes  of  quality  or  quantity.  The  dis- 
covery of  concomitant  variations,  however,  is  of  importance 
in  science,  not  merely  because  it  assists  us  in  determining 
what  events  are  related  as  causes  and  effects,  but  also  be- 
cause the  exact  form  of  the  causal  relation  can  thereby  be 
rendered  more  definite  and  satisfactory.  For  scientific 
knowledge  the  discovery  of  a  '  general  correspondence '  be- 
tween certain  phenomena  is  not  enough;  it  is  necessary  to 
obtain  some  exact  expression  of  the  relation  between  the  two 
sets  of  variations.  This  is  found  by  reducing  the  variations 
to  terms  of  quantity  through  the  application  of  a  common 
unit  of  measurement.  The  law  or  ratio  of  the  variations 
may  then  be  expressed  in  numerical  terms.  Now  the 
scientist  tries  to  include  in  his  statement  of  causal  laws, 
whenever  possible,  precise  information  regarding  the  quanti- 
tative relations  of  the  phenomena  concerned.  Indeed,  we 
may  almost  say  that  science  does  not  exist  until  the  quanti- 
tative aspects  of  phenomena  are  taken  into  account  —  until 
things  are  weighed  and  measured.  The  physicist  does  not 
think  his  work  finished  when  he  has  proved  that  sound  is 
produced  by  atmospheric  vibrations.  He  carries  on  his 
analysis  until  he  can  discover  the  quantitative  relations  be- 
tween the  amplitude  and  velocity  of  the  vibrations,  and  the 
loudness  and  pitch  of  the  resulting  tone.  And  the  psycholo- 
gist is  not  satisfied  with  the  general  statement  that  certain 
sensations  are  causally  connected  with  certain  kinds  of  stim- 
uli; but  he  seeks  to  discover,  whenever  possible,  the  exaat 
quantitative  relation  between    sensation  and   stimulus.  ,  In 


§  62.    The  Method  of  Concomitant    Variations         257 

short,  the  most  important  feature,  the  very  essence,  one 
may  say,  of  modern  scientific  investigation,  is  the  establish- 
ment of  quantitative  relations. 

Looking  at  two  things  with  respect  to  the  order  and  pro- 
gression exhibited  by  their  manner  of  appearance,  then,  we 
say  that  when  their  variations  keep  pace  with  each  other, 
they  are  in  some  way  causally  connected.  What  it  is  neces- 
sary to  establish,  in  order  to  justify  the  inference  to  causal 
relationship,  is  that  there  is  some  definitely  expressible  rela- 
tionship between  the  changes  shown  by  the  two  series.  '  Noth- 
ing is  the  cause  of  a  phenomenon  that  varies  when  the  latter 
is  constant,  or  is  constant  when  it  varies;  or  between  whose 
changes  and  that  of  the  phenomenon  there  is  not  some 
correspondence.'  It  is  not  necessary,  however,  that  the  va- 
riations shown  by  the  two  series  should  always  be  in  the  same 
direction.  One  series,  for  example,  may  increase  as  the 
other  increases,  or  the  two  series  of  changes  may  be  in  in- 
verse ratio.  The  essential  requirement  is  that  there  shall  be 
some  definite  relationship  clearly  made  out  between  the  two 
series  of  events. 

The  following  is  Mill's  statement  of  the  canon:  "  Whatever 
phenomenon  varies  in  any  manner  whenever  another  phenome- 
non varies  in  some  particular  manner,  is  either  a  cause  or  an 
effect  of  that  phenomenon,  or  is  connected  with  it  through 
some  fad  of  causation."  The  illustrations  of  this  law  given 
by  Jevons  are  so  pertinent  that  we  cannot  do  better  than 
adopt  them:  — 

"The  illustrations  of  this  law  are  infinitely  numerous.  Thus 
Mr.  Joule,  of  Manchester,  conclusively  proved  that  friction  is  a  cause 
of  heat  by  expending  exact  quantities  of  force  by  rubbing  one  sub- 
stance against  another,  and  showed  that  the  heat  produced  was 


258  Determination  of  Causal  Relations 

exactly  greater  or  less  in  proportion  as  the  force  was  greater  or  less. 
We  can  apply  the  method  to  many  cases  which  had  previously  been 
treated  by  the  simple  method  of  difference ;  thus  instead  of  striking 
a  bell  in  a  complete  vacuum,  we  can  strike  it  with  a  very  little  air  in 
the  receiver  of  the  air-pump,  and  we  then  hear  a  very  faint  sound 
which  increases  or  decreases  every  time  we  increase  or  diminish  the 
density  of  the  air.  This  experiment  conclusively  satisfies  any  per- 
son that  air  is  the  cause  of  the  transmission  of  sound. 

"It  is  this  method  which  often  enables  us  to  detect  the  material 
connection  which  exists  between  two  bodies.  For  a  long  time  it 
had  been  doubtful  whether  the  red  flames  seen  in  total  eclipses  of 
the  sun  belonged  to  the  sun  or  moon ;  but  during  the  last  eclipse  of 
the  sun,  it  was  noticed  that  the  flames  moved  with  the  sun,  and  were 
gradually  covered  and  uncovered  by  the  moon  at  successive  in- 
stants of  the  eclipse.  No  one  could  doubt  thenceforth  that  they 
belonged  to  the  sun. 

"Whenever,  again,  phenomena  go  through  Periodic  Changes, 
alternately  increasing  and  decreasing,  we  should  seek  for  other  phe- 
nomena which  go  through  changes  in  exactly  the  same  periods,  and 
these  will  probably  be  a  connection  of  cause  and  effect.  It  is  thus 
that  the  tides  are  proved  to  be  due  to  the  attraction  of  the  moon  and 
sun,  because  the  periods  of  high  and  low,  spring  and  neap  tides, 
succeed  each  other  in  intervals  corresponding  to  the  apparent  revo- 
lutions of  those  bodies  round  the  earth.  The  fact  that  the  moon 
revolves  upon  its  own  axis  in  exactly  the  same  period  that  it  revolves 
round  the  earth,  so  that  for  unknown  ages  past  the  same  side  of  the 
moon  has  always  been  turned  toward  the  earth,  is  a  most  perfect 
case  of  concomitant  variations,  conclusively  proving  that  the  earth's 
attraction  governs  the  motions  of  the  moon  on  its  own  axis. 

"The  most  extraordinary  case  of  variations,  however,  consists  in 
the  connection  which  has  of  late  years  been  shown  to  exist  between 
the  Aurora  Borealis,  magnetic  storms,  and  the  spots  on  the  su^ 
It  has  only  in  the  last  thirtv  or  forty  years  become  known  that  the 


§  62.    The  Method  of  Concomitant    Variations         259 

magnetic  compass  is  subject  at  intervals  to  very  slight,  but  curious, 
movements;  and  that,  at  the  same  time,  there  are  usually  natural 
currents  of  electricity  produced  in  telegraph  wires,  so  as  to  interfere 
with  the  transmission  of  messages.  These  disturbances  are  known 
as  magnetic  storms,  and  are  often  observed  to  occur  when  a  fine  dis- 
play of  the  Northern  or  Southern  Lights  is  taking  place  in  some 
part  of  the  earth.  Observations  during  many  years  have  shown 
that  these  storms  come  to  their  worst  at  the  end  of  every  eleven 
years.  .  .  .  Close  observations  of  the  sun  during  thirty  or  forty 
years  have  shown  that  the  size  and  number  of  the  dark  spots,  which 
are  gigantic  storms  going  on  upon  the  sun's  surface,  increase  and 
decrease  exactly  at  the  same  periods  of  time  as  the  magnetic  storms 
upon  the  earth's  surface.  No  one  can  doubt,  then,  that  these  strange 
phenomena  are  connected  together,  though  the  mode  of  the  con- 
nection is  quite  unknown.  .  .  .  This  is  a  most  remarkable  and 
extensive  case  of  concomitant  variations."1 

(1)  In  employing  this  method  it  is,  of  course,  hazardous  to  infer 
the  existence  of  a  universal  law  of  correlation  without  examining  in 
some  detail  the  nature  of  the  concomitant  variations.  In  general 
the  more  definitely  the  relationship  can  be  shown  in  a  consider- 
able number  of  cases,  the  more  ground  there  is  for  the  conclusion 
that  the  conjunction  is  not  accidental.  Moreover,  it  is  also  neces- 
sary that  observations  should  be  extended  over  a  considerable  range 
in  order  to  determine  whether  the  supposed  law  of  correlation  has 
any  limits,  and  if  so  how  they  are  to  be  defined.  For  example,  in 
Weber's  law  we  have  an  exact  expression  for  the  correlation  of  the 
quantity  of  the  stimulus  in  the  case  of  the  various  sense  organs 
and  the  intensity  of  the  resulting  sensation.  But  in  every  case  this 
exact  correlation  of  stimulus  and  sensation  has  an  upper  and  lowei 
limit, beyondwhichit  either  changes  its  character  or  ceases  altogether. 

(2)  The  close  and  almost  inseparable  connection  of  the  different 
methods  in  actual  use,  which  was  emphasized  in  the  preceding  sec- 

1  Jevons,  Lessons  in  Logic,  pp.  249-351. 


260  Determination  of  Causal  Relations 

tion,  is  also  here  clearly  evident.  In  many  fields  it  is  only  through  ex- 
periment that  the  fact  of  correspondences  between  phenomena  can 
be  brought  to  light,  and  the  character  and  law  of  their  correlations 
exactly  determined.  But  to  introduce  experiment  for  these  pur- 
poses is,  of  course,  to  supplement  the  method  of  Concomitant  Vari- 
ations by  the  method  of  Difference.  Similarly,  in  performing  experi- 
ments where  it  is  impossible  to  withdraw  a  certain  element,  and 
thus  by  comparison  to  note  what  its  cause  or  effect  is,  as 
the  strict  canon  of  Difference  requires,  we  may  be  able  to  isolate 
the  element  practically  by  causing  it  to  vary  while  other  circum- 
stances are  kept  constant.  It  is  then  possible  to  note  the  variations 
in  the  corresponding  series  and  thus  to  determine  what  is  causally 
correlated  with  the  element  in  question.  Fo±  example,  if  the  prob- 
lem were  to  determine  the  effect  of  moisture  on  growing  plants 
it  would,  of  course,  be  impossible  to  elimim  +e  moisture  entirely  with- 
out killing  the  plant  and  putting  an  ei.d  to  the  experiment.  But  by 
varying  the  amount  of  moisture,  and  noting  concomitant  changes 
in  the  plant,  both  methods  of  analysis  are  combined. 

§  63.  The  Method  of  Residues.  —  We  have  said  that 
modern  science  employs  measurement  whenever  possible, 
in  order  to  determine  exactly  the  quantitative  relations  of 
phenomena.  Groups  of  facts  whose  connections  are  at  first 
not  perceived,  or  at  best  but  vaguely  apprehended,  are 
brought  into  close  relations  with  one  another  by  the  estab- 
lishment of  definite  quantitative  relations.  The  knowledge 
that  electricity  possesses  energy,  for  example,  is  very  vague 
and  incomplete  when  compared  with  the  definite  equations 
which  the  physicist  can  furnish  between  the  electrical  cur- 
rent generated  under  certain  definite  conditions,  and  the 
amount  of  work  which  it  is  capable  of  performing.  But  the 
discovery  of  quantitative  relations  not  only  renders  our 
knowledge  more  perfect  and  complete,  it  also  enables  us  in. 


§  63.    The  Method  of  Residues  261 

some  cases  to  detect  laws  of  connection  which  would  not 
otherwise  be  observed.  We  have  already  seen  how  the  per- 
ception of  corresponding  changes  in  the  quantities  of  phe- 
nomena has  led  to  the  discovery  of  causal  laws  by  means 
of  the  method  of  Concomitant  Variations.  The  method  of 
Residues,  which  we  now  have  to  discuss,  is  also  largely 
dependent  on  quantitative  determination. 

In  general,  this  method  calls  attention  to  any  remainder 
or  residue  which  is  left  over  after  other  portions  of  a  complex 
phenomenon  have  been  explained.  There  are  two  results 
of  this  method  which  may  be  discussed  separately. 

(a)  The  application  of  this  method  to  a  complex  phenom- 
enon which  is  the  result  of  several  causes,  often  enables  us 
to  determine  what  part  each  of  these  causes  plays  in  the 
determination  of  the  whole  fact  under  consideration.  Mill's 
fifth  canon  seems  to  apply  to  this  case.  It  is  as  follows: 
Subduct  from  any  phenomenon  such  part  as  is  known  by  pre- 
vious inductions  to  be  the  effect  of  certain  antecedents,  and  the 
residue  of  the' phenomenon  is  the  effect  of  the  remaining  ante- 
cedents. Thus,  if  it  is  known  that  the  complex  phenomenon 
BAC  is  the  result  of  bac,  and  if  it  is  further  known  that  a  is 
the  cause  of  A,  and  b  of  B,  it  follows,  of  course,  by  sub- 
traction that  the  residue  still  unexplained,  C,  is  caused  by 
c,  the  remaining  antecedent. 

Of  course  the  application  of  this  method  in  concrete  cases  does 
not  usually  resolve  itself  into  such  a  simple  process  of  subtraction. 
It  requires  work  —  'previous  inductions,'  as  Mill  says  —  to  deter- 
mine what  are  the  whole  number  of  antecedents  in  any  case,  as  well 
as  to  isolate  the  various  antecedents  so  as  to  determine  exactly  what 
part  of  the  effect  is  to  be  ascribed  to  each  one.  This  may  be  illus- 
trated by  an  example :  after  my  student's  lamp  has  been  lighted  two 


262  Determination  of  Causal  Relations 

hours,  I  find  the  thermometer  has  risen  from  650  to  700  Fahr.  The 
phenomenon  to  be  explained  then  is  the  additional  50  of  heat. 
There  is  no  fire,  and  it  seems  that  the  increase  in  temperature  must 
be  due  to  the  lamp,  and  the  heat  given  off  from  my  body  during 
this  period.  Suppose  that  the  lamp  is  burned  for  the  same  length 
of  time  while  the  room  is  unoccupied,  all  other  conditions  remaining 
the  same,  and  that  the  thermometer  shows  an  increase  of  40  in  the 
temperature.  By  subtraction  we  could  conclude  that  the  heat  given 
off  by  the  body  on  the  former  occasion  was  the  cause  of  the  addi- 
tional degree  of  temperature. 

To  carry  the  process  of  analysis  a  step  further.  Let  us  suppose 
that  a  half  pint  of  oil,  which  is  composed  of  hydrogen  and  carbon, 
has  been  consumed.  We  could  determine,  by  measuring  the  heat 
produced  by  the  oxidation  of  the  exact  amount  of  carbon  contained 
in  one-half  a  pint  of  oil,  what  quantity  of  heat  is  due  to  the  com- 
bustion of  the  carbon  contained  in  the  oil,  and,  by  subtraction, 
what  must  be  ascribed  to  the  burning  of  the  hydrogen.1 

(b)  The  second  case  in  which  this  method  may  be  applied 
is  where  there  is  an  unexplained  remainder  or  residue  left 
over  after  the  result  of  all  the  known  causes  has  been  calcu- 
lated. Mill  does  not  distinguish  between  such  instances 
and  the  method  of  simple  subtraction  discussed  above. 
Since,  however,  the  cause  must  explain  the  whole  of  the 
effect,  the  method  of  residues  enjoins  us  to  continue  the  search 
for  explanation.  When  any  part  of  a  complex  phenomenon 
is  still  unexplained  by  the  causes  which  have  been  assigned,  a 
further  cause  for  this  remainder  must  be  sought.  If,  for  ex- 
ample, it  were  found  by  actual  measurement  that  the  heat 
produced  by  the  lamp,  and  by  the  body  of  the  occupant,  were 

1  This  is,  of  course,  not  strictly  correct,  for  it  leaves  out  of  account  the 
heat  generated  by  the  chemical  combination  of  the  carbon  and  hydrogen. 
It  may,  therefore,  serve  to  illustrate  a  case  where  the  method  of  Residues 
breaks  down. 


§  63.    The  Method  of  Residues  263 

not  sufficient  to  account  for  the  change  in  temperature  of  the 
room,  it  would  be  necessary  to  seek  for  some  further  cause 
to  account  for  this  unexpected  remainder. 

This  method  can  scarcely  be  said  to  be  more  than  a  de- 
mand for  complete  and  precise  explanation.  The  attempt, 
however,  to  account  for  unexplained  residues  has  led  to 
many  extremely  important  discoveries  in  science.  Residual 
phenomena  are  often  so  obscure,  and  appear  so  uninterest- 
ing and  unimportant  to  the  ordinary  mind,  that  they  are 
passed  over  without  explanation.  It  usually  requires  the 
eye  of  a  scientific  genius  to  see  the  importance  of  things 
which  appear  trivial  and  unessential.  With  Darwin,  facts 
which  might  appear  to  an  ordinary  observer  mere  unimpor- 
tant exceptions,  were  made  the  object  of  special  attention, 
and  often  served  as  starting-points  for  his  investigations. 
Francis  Darwin,  speaking  of  his  father,  says:  "There  was 
one  quality  of  mind  which  seemed  to  be  of  special  and  ex- 
treme advantage  in  leading  him  to  make  discoveries.  It 
was  the  power  of  never  letting  exceptions  pass  unnoticed. 
...  A  point  apparently  slight  and  unconnected  with  his 
present  work  is  passed  over  by  many  a  man  almost  uncon- 
sciously, with  some  half-considered  explanation,  which  is 
really  no  explanation.  It  was  just  these  things  that  he 
seized  upon  to  make  a  start."  l 

Among  the  many  important  discoveries  which  have  resulted  from 
the  investigation  of  some  obscure  and  seemingly  unimportant  fact, 
we  may  mention  that  of  ozone.  It  had  been  observed  for  a  long 
time  that  the  passage  of. electric  sparks  through  the  air  is  accom- 
panied by  a  peculiar  odour.  This  odour  was  also  found  near 
electrical  machines,  and  was  known  as  the  'electrical  smell.'  No 
1  Life  and  Letters  of  Charles  Darwin,  Vol.  I.,  p.  125. 


264  Determination  of  Causal  Relations 

one  seemed  to  have  attached  any  importance  to  it  or  to  have  at- 
tempted to  explain  it  in  any  way,  until  Friedrich  Schonbein,  a  pro- 
fessor of   chemistry  at  Basel,  turned  his  attention  to  the  subject. 
The  result  of  his  investigations  was  the  discovery  of   ozone,  the 
peculiar  modification  of  oxygen,  which  was  the  cause  of  the  odour. 
Another  very  striking  example  of  the  application  of  this  method 
is  afforded  by  the  history  of  the  discovery  of  the  planet  Neptune. 
In  1 781  a  new  planet  was  discovered  moving  outside  all  the  other 
planets  by  Sir  William  Herschel.     This  was  the  planet  Uranus. 
When  its  orbit  came  to  be  calculated,  it  was  found  that  it  did  not 
move  as  it  might  be  expected  to  do  according  to  the  theory  of  gravi- 
tation.    That  is,  the  attraction  of  the  sun  and  the  known  planets  did 
not  account  for  the  path  it  took :   it  moved  outwards  into   space 
farther  than  it  ought  to  have  done.     It  was  evident  that  either  some 
mistake  must  have  been  made  in  the  observation  of  the  astronomers, 
or  some  unknown  body  must  be  dragging  it  out  of  its  course.     No 
traces  of  any  such  planet  could  be  perceived,  and  the  problem 
remained  unsolved.     In   1843,  a  student  of  St.  John's  College, 
Cambridge,  named  Adams,  undertook  to  work  out  the  movements 
of  Uranus,  to  discover,  if  possible,  the  position  of  the  body  which 
was  pulling  it  out  of  what  would  otherwise  be  its  proper  path,  the 
attractions  exercised  by  the  sun  and  the  planets  in  their  different 
positions,  and  to  show  what  effect  they  would  have  in  determining 
the  orbit  of  Uranus.     Whenever  the  planet  was  deflected  outwards, 
it  was  necessary  to  show  where  the  body  was  situated  which  was 
thus  influencing  it.     In  1845  he  was  able  to  send  a  paper  to  the 
astronomer  royal  at  Greenwich,  informing  him  in  what  quarter  of 
the  heavens  the  new  planet  should  be  observed.     When  the  discov- 
ery was  afterwards  made,  it  was  proved  that  his  calculations  were 
almost  exactly  correct.     A  failure  on  the  part  of  the  astronomer 
royal  to  cooperate  by  looking  through  his  telescope  for  the  planet 
gave  the  prior  right  of  discovery  to  a  Frenchman  named  Leverrier. 
The  latter  worked  out  his  calculations  in  the  same  way  as  Adams.. 


§  63.    The  Method  of  Residues  265 

and  obtained  almost  exactly  the  same  results.  He  sent  these  results 
to  Professor  Galle  of  the  Berlin  University  on  the  23d  September, 
1864,  asking  him  to  look  in  the  part  of  the  heavens  which  he 
indicated.  That  same  evening,  by  following  out  the  directions,  the 
planet  was  discovered  in  almost  the  exact  spot  predicted.1 

The  history  of  this  discovery  illustrates  as  well  several  methods 
and  processes  which  we  have  not  yet  discussed,  such  as  the  forma- 
tion and  verification  of  hypotheses.  It  is  also  interesting  as  showing 
how  reason  is  able,  under  certain  conditions,  to  anticipate  per- 
ception. The  relations  and  forces  of  the  heavenly  bodies  had 
been  so  perfectly  formulated  in  the  law  of  gravitation  that  these 
two  investigators,  working  in  their  studies,  were  able  to  predict 
not  only  the  presence,  but  the  exact  position  of  a  planet  which  up 
to  that  time  had  never  been  observed.  It  is  where  mathematical 
methods  can  be  used  that  such  anticipation  is  most  often  possible. 
Hence  this  use  of  the  method  of  Residues  has  frequently  led  to 
important  results  in  astronomy. 

REFERENCES  TO  CHAPTERS  XV.  AND  XVI. 

Mill,  Logic,  Bk.  III.,  Chs.  VIII.  and  IX. 

Joseph,  An  Introduction  to  Logic,  Ch.  XX. 

Sigwart,  Logic,  Vol.  II.,  §  95. 

Hobhouse,  The  Theory  of  Knowledge,  Chs.  XIII.-XV. 

1  Cf .  Clerke,  A  Popular  History  of  Astronomy  during  the  Nineteenth 
Century,  pp.  96  ff. ;  Buckley,  A  Short  History  of  Natural  Science,  pp.  302  ff. 


CHAPTER    XVIII 


ANALOGY 


§  64.  Explanation  by  Analogy. — An  'Analogy'  may  be 
denned  in  general  terms  as  an  agreement,  resemblance,  or 
proportion  between  the  relations  of  things  to  one  another,  or 
between  the  things  themselves.  Thus  it  might  be  said  that 
there  is  an  analogy  between  the  relations  of  a  ruler  to  his 
people  and  those  of  the  captain  of  a  vessel  to  members  of  his 
crew.  Or  an  analogy  might  be  said  to  exist  simply  between 
a  ruler  and  a  captain,  or  between  a  state  and  a  ship.  In  logic, 
analogy  is  used  more  specifically  as  a  form  of  reasoning  in 
which,  from  the  resemblances  of  two  or  more  things  in  certain 
respects,  their  likeness  in  other  respects  is  inferred. 

The  tendency  to  note  resemblances  and  to  assume  that 
things  alike  in  certain  respects  are  alike  in  all,  is  present  from 
the  first  in  all  stages  of  thinking.  We  have  seen  (§  50)  that 
this  principle  guides  inductive  inquiry  by  furnishing  sugges- 
tions as  to  what  may  be  expected  when  new  facts  and  condi- 
tions are  met  with.  But  in  noting,  in  our  earlier  discussion, 
the  operation  of  this  principle,  no  detailed  description  of  its 
principles  was  given,  or  any  adequate  account  of  the  part  it 
plays  in  organizing  experience.  In  this  chapter  emphasis  is 
laid  more  particularly  on  the  function  that  Analogy  performs 
at  a  somewhat  advanced  stage  of  inductive  inquiry,  in  leading 
on  to  the  higher  generalizations  of  science.  At  a  lower  level 
the  connections  and  relations  suggested  by  Analogy  are  of  a 

266 


§  64.    Explanation  by  Analogy  267 

factual  and  descriptive  character.  For  example,  Analogy 
might  suggest  in  a  particular  case  that  the  severe  frost  is  the 
cause  of  the  bursting  of  water  pipes,  without  affording  any 
clear  understanding  of  the  universal  law  through  which  these 
things  are  connected.  In  more  advanced  stages  of  know- 
ledge, however,  Analogy  is  used  consciously  and  critically  as 
a  means  of  deriving  general  laws  and  principles  of  explana- 
tion. In  proceeding  to  the  discussion  of  this  more  explicit 
use  of  Analogy,  we  may  then  be  said  to  be  passing  from 
Description  to  Explanation.  But,  as  has  already  been 
pointed  out  (§§  52,  53),  no  hard  and  fast  line  can  be  drawn 
between  the  determination  of  the  nature  and  connection  of 
facts,  and  their  explanation.  The  task  which  our  thought 
is  called  upon  to  perform  is  to  transform  obscurely  known 
and  isolated  facts  into  an  orderly  and  consistent  system  of 
knowledge,  and  this  process  is  continuous  throughout.  But, 
keeping  this  in  mind,  one  may  still  say  that  it  is  necessary, 
in  the  first  place,  for  the  facts  to  be  thoroughly  analyzed  and 
carefully  examined;  and,  secondly,  for  them  to  be  grouped 
together  according  to  some  general  principle  or  principles 
which  shall  make  clear  and  intelligible  the  relations  in  which 
they  stand  to  one  another. 

To  explain  is  just  to  show  that  some  fact  or  group  of  facts 
is  related  to  some  other  fact  or  group  with  which  we  are  ac- 
quainted. So  far  as  the  methods  we  have  discussed  enable  us 
to  establish  connections  between  events,  they  may  fairly 
claim  to  be  methods  of  explanation.  Nevertheless,  although 
the  difference  between  these  methods,  and  those  of  explanation 
in  terms  of  wider  generali7ations,  is  one  of  degree  rather  than 
of  essential  nature,  it  is  important  to  keep  it  in  mind.  The 
canons  which  were  stated  in  the  last  two  chapters  —  what 


268  Analogy 

Mill  named  the  experimental  methods  —  are  rules  for  deter- 
mining causal  connections  between  phenomena.  The  prob-  . 
lem  in  those  chapters  was  to  determine  what  particular 
phenomena  of  our  experience  are  essentially  and  necessarily 
connected  as  antecedents  and  consequents.  This  constitutes 
a  more  or  less  distinct  step  in  the  work  of  systematization 
which  is  carried  on  by  thought.  The  method  of  Difference, 
for  instance,  enables  us  to  say  that  hot  water  will  break  thick 
glasses  when  poured  into  them,  but  will  not  damage  thin 
ones.  '  So  much  for  the  fact'  we  say,  '  but  the  explanation  is 
still  wanting.'  We  must  try  to  make  the  fact  intelligible  by 
going  outside  of  it,  and  showing  that  this  behaviour  on  the 
part  of  the  glasses  is  simply  a  case  or  illustration  of  what  we 
already  know  of  the  properties  of  bodies  when  heated. 
Again,  the  method  of  Concomitant  Variations,  as  we  have  seen 
from  Jevons's  example,  has  led  us  to  believe  in  some  causal 
connection  between  electrical  storms,  sun-spots,  and  the 
Aurora  Borealis.  In  this  instance,  knowledge  has  not  been 
able  to  advance  beyond  the  fact  to  its  explanation.  No  satis- 
factory theory  has  yet  been  established  to  account  for  the  un- 
doubted fact  that  these  phenomena  are  in  some  way  causally 
connected. 

The  principle  of  Analogy  is  resemblance.  The  phenome- 
non to  be  explained  is  connected  with  some  more  familiar 
occurrence  through  a  perceived  or  imagined  likeness  between 
the  two  cases.  All  our  first  rude  classifications  and  explana- 
tions are  based  on  this  principle.  In  the  early  stages  of  the 
history  of  the  race,  everything  was  explained  on  the  analogy  of 
human  actions  (cf.  §  89).  All  natural  events,  that  is,  were 
supposed  to  be  produced  by  superhuman  agents,  who  were, 
however,  endowed  with  essentially  the  same  qualities  as  man. 


§  64.    Explanation  by  Analogy  269 

In  the  thunder,  the  men  of  a  primitive  age  heard  the  voice 
of  a  god.  An  eclipse  of  the  sun  or  moon  was  interpreted  as 
a  divine  sign  or  warning.  When  the  sea  became  tempestuous 
and  lashed  its  shores,  they  believed  that  the  sea-god  was  angry. 
In  every  case,  they  interpreted  these  mysterious  happenings 
of  nature  by  referring  them  to  causes  similar  in  character  to 
those  which  they  best  understood  as  effective  forces — the 
motives  and  volitions  of  themselves  and  their  fellows. 

The  principle  of  analogy  is  employed  in  the  same  way  in 
modern  times.  It  is  true  that  we  no  longer  think  that  natural 
events  are  directly  caused  by  the  action  of  some  spiritual  agent 
more  or  less  like  ourselves.  But,  when  we  endeavour  to  show 
that  the  phenomena  which  we  are  interested  to  explain  are 
similar  in  important  respects  to  some  group  of  facts  with 
whose  mode  of  operation  we  are  familiar,  we  proceed  by 
analogy.  On  the  basis  of  this  similarity,  we  argue  that  the 
phenomena  with  which  we  are  dealing  probably  have  the 
same  properties,  or  operate  in  the  same  way,  or  are  governed 
by  the  same  laws,  as  the  better-known  facts  which  they  re- 
semble. The  formula  of  analogy  may  be  stated  in  this  way: 
Two  things  resemble  each  other  in  one  or  more  respects,  they 
are  therefore  of  the  same  general  type  or  character;  it  follows 
that  a  certain  proposition  which  is  true  of  the  one  is  prob- 
ably true  of  the  other.  The  following  example  of  analogy 
has  been  frequently  used  as  an  illustration:  — 

"We  may  observe  a  very  great  similitude  between  this  earth 
which  we  inhabit,  and  the  other  planets,  Saturn,  Jupiter,  Mars, 
Venus,  and  Mercury.  They  all  revolve  round  the  sun,  as  the  earth 
does,  although  at  different  distances  and  in  different  periods.  They 
borrow  all  their  light  from  the  sun,  as  the  earth  does.  Several  of 
them  are  known  to  revolve  around  their  axes  like  the  earth,  and  by 


270  Analogy 

that  means  must  have  a  like  succession  of  day  and  night.  Some  of 
them  have  moons  that  serve  to  give  them  light  in  the  absence  of  the 
sun,  as  our  moon  does  to  us.  They  are  all  in  their  motions  subject 
to  the  same  law  of  gravitation  as  the  earth  is.  From  all  this  simili- 
tude, it  is  not  unreasonable  to  think  that  those  planets  may,  like 
our  earth,  be  the  habitation  of  various  orders  of  living  creatures. "  * 
The  word  'analogy'  at  the  present  time  is  somewhat  loosely 
used  for  any  mark  of  similarity  or  resemblance  which  enables  us 
to  reason  from  one  thing  to  another.  As  already  noted,  the  term 
is  also  applied  either  to  a  likeness  between  two  things,  or  a  likeness 
between  certain  relations  of  things.  In  the  latter  case,  there  is  of 
course  a  proportion  expressed,  as  when  it  is  said  that  the  relation 
of  a  clergyman  to  his  parishioners  is  analogous  to  that  of  a  physi- 
cian to  his  patients.  The  purpose  of  such  comparisons  is  to 
afford  a  basis  for  inferring  that  the  rights  or  duties  -that  exist  in 
the  one  case  obtain  also  in  the  other.  In  such  cases,  however, 
we  have  always  to  ask  if  there  are  not  differences,  as  well  as 
likenesses,  in  the  two  sets  of  relations.  This  employment  of 
analogy  is  more  strictly  that  which  was  noted  and  defined  by 
Aristotle.  "The  original  word  avaXoyia,  as  employed  by  Aris- 
totle, corresponds  to  the  word  Proportion  in  Arithmetic ;  it  signi- 
fies an  equality  of  ratios,  IcroTrfi  \6ywv.  two  compared  with  four  is 
analogous  to  four  compared  with  eight.  There  is  something  oi 
the  same  meaning  in  the  technical  use  of  the  word  in  physiology, 
where  it  is  used  to  signify  similarity  of  function  as  distinguished 
from  similarity  of  structure,  which  is  called  homology ;  thus  the  tail 
of  a  whale  is  analogous  to  the  tail  of  a  fish,  inasmuch  as  it  is  simi- 
larly used  for  motion,  but  is  homologous  with  the  hind  legs  of  a 
quadruped.  A  man's  arms  are  homologous  with  a  horse's  fore 
legs,  but  they  are  not  analogous,  inasmuch  as  they  are  not  used  for 
progression."2 

1  Reid,  Intellectual  Powers  of  Man,  Essay  I.,  Ch.  Ill, 
1  Minto,  Logic,  Inductive  and  Deductive,  p.  367. 


§  65.   Analogy  and  Explanatory  HypotJieses         271 

Apart  from  these  technical  uses,  what  is  known  as  analogical 
reasoning  may,  perhaps,  be  best  defined  as  an  argument  from 
similar  instances.  In  analogy,  we  do  not  stop  to  work  out  a 
law  of  connection  between  phenomena  by  comparing  a 
number  of  cases,  or  by  using  any  of  the  ordinary  inductive 
canons.  But  finding  a  striking  resemblance  between  some 
circumstance  —  relation,  quality,  arrangement,  function,  etc. 

—  in  the  phenomena  to  be  explained,  and  some  phenomena 
with  which  we  are  already  acquainted,  we  use  the  latter  as 
a  basis  for  conclusions  about  the  former.  Analogy  is  thus 
an  argument  from  examples  or  instances,  its  value  depending 
upon  the  real  identity  in  some  important  aspect  of  the  cases 
compared.  When,  however,  our  thought  is  able  to  extend  to 
a  new  case,  or  set  of  cases,  some  general  law  or  principle 
with  whose  operation  it  is  already  acquainted  in  other  in- 
stances, we  have  passed  beyond  analogy  to  a  higher  form  of 
explanation.  In  the  former  case,  we  argue  from  the  resem- 
blance of  instances;  in  the  latter,  the  thread  which  binds 
the  new  instance  with  the  old  is  the  identity  of  a  general 
principle. 

§  65.    Analogy  as  Suggestive  of  Explanatory  Hypotheses. 

—  We  have  shown  above  that  analogical  reasoning  depends  on 
the  resemblance  which  exists  between  individual  cases  or 
instances,  and  that  it  does  not  itself  succeed  in  formulating 
any  general  law  or  principle.  The  next  section  will  show 
in  more  detail  in  what  respects  the  principle  of  analogy  falls 
short,  and  why,  taken  by  itself,  it  can  only  be  regarded  as 
incomplete  explanation.  Here  we  have  to  notice  the  im- 
portant part  which  it  plays  in  suggesting  laws  and  principles. 
Although  analogy  '  sticks  in  the  particular  instances,'  it  leads 
the  mind  on  to  general  laws  and  explanatory  theories.     It  is 


272  Analogy 

thus  of  the  greatest  importance  as  a  necessary  stage  on  ths 
way  to  complete  explanation. 

When  we  are  able  to  discover  some  general  resemblance 
between  a  group  of  phenomena  which  we  are  interested  to 
explain,  and  another  group  whose  principle  of  operation  we 
already  understand,  our  thought  strives  to  extend  the  known 
principle  and  to  bring  the  new  facts  under  it.    The  unknown 
or  unexplained  facts  are  thus  brought  under  a  known  law.     It 
is  of  course  true  that  the  application  of  the  law  to  a  new  set  of 
facts  broadens  our  conception  of  its  scope,  and  often  requires 
us  to  state  it  in  a  more  adequate  way.    Thus  the  analogy 
which  Newton  perceived  between  the  heavenly  bodies  falling 
through  space  and  the  falling  of  the  apple  towards  the  ground, 
led  to  the  formulation  in  exact  mathematical  terms  of  the 
universal  law  of  gravitation.    Our  knowledge  of  the  various 
functions   of    plants  —  digestion,    reproduction,    etc.  —  has 
been  obtained  by  ascribing  to  the  various  organs  of  the  plant, 
purposes  analogous  to  those  which  are  fulfilled  by  the  parts 
of  animal  bodies.     And,  in  turn,  the  study  of  plant  physiology 
has  thrown  light  upon  animal  physiology,  and  enlarged  and 
modified  many  of  its  theories.     Again,  the  explanation  of 
many  geological  changes,  — the  wearing  away  of  rocks,  the 
formation  of  deltas  or  of  great  ravines,  of  vegetable  mould, 
etc.,  —  is  facilitated  by  a  discovery  of  their  analogy  with 
familiar  events  which  happen  constantly  before  our  eyes. 

An  extremely  interesting  instance  of  the  part  which  analogy 
plays  in  suggesting  possible  explanations,  is  found  in  the  account 
of  the  discovery  of  the  principle  of  Natural  Selection  given  by  Dar- 
win in  his  Autobiography.  In  1837  Darwin  opened  a  note-book 
for  the  purpose  of  recording  all  facts  in  any  way  connected  with  the 
variation  of  species  in  nature  and  under  domestication.     He  first 


§  65.   Analogy  and  Explanatory  Hypotheses         273 

investigated  the  variations  of  plants  and  animals  which  are  produced 
under  domestication,  by  printed  inquiries,  by  conversation  with 
skilful  breeders,  and  by  extensive  reading.  "I  soon  found,"  he  says, 
"that  selection  was  the  keystone  of  man's  success  in  making  useful 
races  of  plants  and  animals. "  When  useful  or  pleasing  varieties 
of  plants  or  animals  occur,  the  gardener  or  breeder  preserves  them, 
and  their  peculiar  qualities  are  transmitted  to  their  offspring.  And, 
in  a  number  of  generations,  these  qualities  become  more  pronounced 
through  accumulation.  The  differences  between  varieties  of  the 
same  species  of  domesticated  animals  —  varieties  which  are  as  differ- 
ent, for  example,  as  the  mastiff  and  Skye  terrier  —  are  due  to  the 
selective  agency  of  man.  But  is  there  anything  analogous  takes 
place  on  an  indefinitely  larger  scale  in  nature?  If  so,  what  is  it 
which  plays  the  part  of  the  gardener  or  breeder,  and  preserves 
certain  varieties  ? 

When  Darwin  had  reached  this  point  in  his  investigations,  and, 
had  come  to  appreciate  what  selection  could  do,  he  happened  to 
read  Malthus's  book,  On  Population.  The  purpose  of  this  book 
was  to  dispel  the  optimistic  ideas  of  some  of  the  writers  of  the 
eighteenth  century  who  looked  for  the  speedy  realization  of  social 
welhbeing  and  happiness.  Such  an  ideal  is  impossible  of  fulfilment, 
said  Malthus,  because  of  the  inevitable  tendency  of  population  to 
increase  faster  than  the  supply  of  food.  Human  beings  increase  in 
a  geometrical  ratio ;  the  means  of  subsistence,  at  best,  only  by  an 
arithmetical  ratio.  The  population  will  thus  constantly  tend  to 
exceed  the  limit  of  the  food  supply,  and  will  be  kept  in  check  only 
by  starvation.  A  constant  struggle  for  food  is  the  lot,  then,  to 
which  each  individual  is  doomed  in  virtue  of  this  law.  Darwin's 
observations  of  the  rate  at  which  plants  and  animals  tend  to  repro- 
duce their  kind,  led  him  at  once  to  extend  Malthus's  principle  to 
the  whole  of  nature.  The  fecundity  of  natural  beings  leads  to  a 
struggle  for  existence,  not  merely  among  men,  but  throughout  the 
whole  organic  world.     And  if  there  is  a  struggle,  we  have  natural 


274  Analogy 

selection  or  the  survival  of  the  fittest.  Darwin  saw  "that  natural 
selection  was  the  inevitable  result  of  the  rapid  increase  of  all  organic 
beings. "  It  is  not  difficult  to  see  that  this  discovery  was  the  result 
of  Darwin's  wonderful  power  of  perceiving  analogies  between  differ- 
ent classes  of  facts.  His  genius  led  him  to  recognize  first  the  re- 
semblance of  the  variations  of  species  in  nature  to  the  more  familiar 
variations  which  go  on  among  domesticated  plants  and  animals. 
And,  secondly,  he  perceived  that  the  competition  for  the  means  of 
subsistence,  which  the  pressure  of  populationimposes  upon  the  mem- 
bers of  the  human  race,  is  simply  one  phase  of  'the  struggle  for 
existence,'  which  is  going  on  everywhere  throughout  the  organic 
world. 

§  66.    The    Incompleteness   of   Analogical    Reasoning.— 

The  most  striking  feature  of  analogical  arguments  is  found  in 
the  fact  that  they  yield  only  probable  conclusions.  And  the 
reason  for  this  is  not  far  to  seek.  For,  as  has  been  already 
shown,  analogy  is  a  method  of  reasoning  from  one  particular 
case  to  another  on  the  basis  of  some  imagined  or  perceived 
similarity  between  the  two  cases.  Complete  logical  demon- 
stration, or  certainty,  however,  is  attained  only  when  the  new 
fact  or  group  of  facts  is  really  and  essentially  united  by  means 
of  some  general  principle  with  what  is  already  known.  There 
is  no  genuine  inference  from  'particular  to  particular,'  as 
Mill  supposed.  Inference,  as  has  been  well  said,  always 
'  proceeds  through  a  universal'  It  is  the  universal  implied 
in  the  common  name,  or  vaguely  present  in  the  mind  of  the 
reasoner,  which  really  carries  the  inference  in  cases  where 
conclusions  appear  to  be  drawn  from  a  particular  case. 
When  one  reasons  that  food  or  drink  which  has  made  A 
ill  will  produce  the  same  result  in  B,  it  is  the  universal  nature 
of  human  beings  on  which  the  inference  is  based.     In  the 


§  66.    Incompleteness  of  Analogical  Reasoning      275 

case  of  Analogy,  the  inference  lacks  certainty  because 
the  universal  nature  is  not  analyzed  or  defined.  Instead, 
it  is  vaguely  assumed  in  the  form  of  external  likeness  or 
resemblance. 

But,  although  Analogy  yields  only  probable  conclusions, 
it  must  not  be  forgotten  that  '  probability '  is  not  a  fixed 
quantity.  An  argument  from  analogy  may  have  any  degree 
of  value,  from  zero  almost  up  to  the  limit  of  complete  logical 
certainty.  To  fully  explain  or  demonstrate  any  fact,  we  are 
obliged,  I  think,  to  go  beyond  analogy,  and  to  verify  its  con- 
clusions by  a  method  which  has  still  to  be  described.  It  is 
evident,  nevertheless,  that  the  value  of  an  analogical  argu- 
ment will  depend  upon  the  nature  of  the  resemblance  which 
is  taken  as  the  basis  of  inference.  In  general,  it  is  true  that 
the  greater  the  resemblance  between  the  two  cases,  the  more 
certainly  can  we  reason  from  one  to  the  other.  This  is  not  to 
say,  however,  that  the  value  of  the  conclusion  is  in  direct 
proportion  to  the  number  of  points  of  resemblance  which  can 
be  discovered.  For  example,  we  might  reason:  These  two 
men  are  of  the  same  height,  of  the  same  age,  live  in  the  same 
house,  come  from  the  same  town;  the  one  man  stands  well 
in  his  classes,  therefore  the  other  probably  does  so  also. 
If  the  number  of  points  of  resemblance  were  the  essential 
thing,  the  argument  ought  to  possess  some  weight,  but  it  is 
clear  that  it  has  none.  The  difficulty  is  that  none  of  the 
resemblances  mentioned  are  fundamental,  or  in  any  way 
essential  to  the  real  nature  of  the  things  compared.  If  we 
knew  that  the  two  men  were  similar  in  character,  this  one 
characteristic  would  be  worth  more,  as  a  basis  for  the  con- 
clusion, than  all  the  circumstances  which  we  have  mentioned 
combined. 


276  Analogy 

It  is  true,  then,  as  Mr.  Bosanquet  remarks,  that  in  analogi- 
cal reasoning  we  must  weigh  the  points  of  resemblance  rather 
than  count  them.1  Other  things  being  equal,  the  more  pointi 
of  resemblance  we  can  make  out  the  better;  but  if  these  are 
to  contribute  at  all  to  the  certainty  of  the  conclusion,  they 
must  represent  some  deep-lying  characteristic  of  the  things 
compared.  In  general,  it  must  be  said  that  it  is  only  expe- 
rience which  can  inform  us  what  resemblances  are  fundamen- 
tal, and  what  merely  external.  Systematic  knowledge  in  any 
field  enables  us  to  separate  the  essential  from  the  accidental. 
And,  what  is  perhaps  a  corollary  from  this,  it  must  not  be 
forgotten  that  the  value  of  an  inference  from  analogy  depends 
largely  upon  the  amount  of  intellectual  insight  possessed  by 
the  mind  which  makes  it.  The  ordinary  mind,  at  least  in  its 
undisciplined  and  untutored  condition,  regards  all  things  as  of 
equal  importance.  It  is  therefore  led  away  by  the  strongest 
stimulus — by  striking  external  and  accidental  resemblances 
—  as  is  well  shown  by  the  readiness  with  which  such  minds 
are  carried  away  by  the  fallacies  of  figurative  or  analogical 
language.  On  the  other  hand,  a  scientific  genius  whose  mind 
is  well  stored  with  facts,  and  who  is  gifted  in  addition  with 
imagination,  is  able  to  penetrate  beneath  the  surface  and  to 
apprehend  the  real  or  fundamental  resemblance.  His  imagi- 
nation enables  him  to  see  beyond  the  chaos  of  the  particular 
facts,  and  to  detect  the  underlying  principle  by  means  of 
which  these  facts  can  be  connected  and  systematized. 

Analogy  thus  becomes  deepened  until  it  passes  from  the 

stage  of  a  mere  argument  from  particular  to  particular,  to 

the  perception  of  a  general  law  which  includes  the  individual 

instance.     But  no  such  direct  insight  can  claim  the  title  of 

1  Logic,  Vol.  II.,  p.  99. 


§  66.    Incompleteness  of  Attn  logical  Reasoning     277 

knowledge,  until  it  is  tried  and  tested  by  the  facts.  The 
guesses  of  scientific  men  unfortunately  often  prove  mistaken. 
It  is  always  necessary  that  fancy  shall  be  confronted  with 
facts.  Even  Darwin's  magnificent  analogical  inference  was 
nothing  more  than  an  hypothesis,  as  he  himself  well  under- 
stood, until  its  power  of  explaining  the  facts  of  organic  life 
was  demonstrated.  We  have  now  to  explain  in  the  next 
chapter  the  methods  by  which  such  guesses  are  tested. 

REFERENCES 

J.  S.  Mill,  Logic,  Bk.  III.,  Ch.  XX 

A.  Bain,  Logic,  Part  Second,  Induction,  pp.  140-148. 
J.  G.  Hibben,  Inductive  Logic,  Ch.  XIV. 

B.  Bosanquet,  Logic,  Vol.  II.,  Ch.  III. 

"         The  Essentials  of  Logic,  pp.  155-58. 
W.  Minto,  Logic  Inductive  and  Deductive,  pp.  367-373. 


CHAPTER   XIX 

THE    USE    OF   HYPOTHESES 

§  67.  Reasoning  from  an  Hypothesis.  — An  hypothesis, 
taken  in  its  most  general  sense,  is  a  guess  or  supposition  as 
to  the  existence  of  some  fact  or  law  which  will  serve  to  explain 
a  fact  or  connection  of  facts  already  known  to  exist.  It  is 
thus  an  expression  of  the  tendency  of  the  mind  to  leave  noth- 
ing standing  in  isolation,  but  to  '  explain  '  the  various  parts  of 
experience  by  bringing  them  into  relation  with  one  another. 
'Theory  '  is  another  word  that  is  often  used  as  equivalent  to 
hypothesis.  Strictly  speaking,  however,  it  is  better  usage  to 
employ  the  term  '  hypothesis  '  for  the  unverified,  or  only  par- 
tially verified  guess,  and  to  reserve  '  theory'  for  the  hypothesis 
that  has  been  more  completely  demonstrated.  This  distinc- 
tion, however,  is  not  usually  maintained,  and  even  in  scientific 
writings  the  terms  '  theory  '  and  '  hypothesis  '  are  used  in- 
terchangeably. Nevertheless,  it  is  necessary  to  distinguish 
in  some  way  the  '  mere  hypothesis,'  or  supposition,  which  is 
often  as  likely  to  be  false  as  true,  from  the  hypothesis  which 
has  been  established  by  proof. 

It  is  important  to  remember  that  it  is  not  only  in  solving 
scientific  problems  that  we  employ  hypotheses.  In  our  ordi- 
nary experience,  we  are  constantly  trying  to  imagine  the 
most  likely  explanation  of  facts  which  we  perceive  through 
the  senses.  If,  for  example,  one  should  find  on  returning 
to  one's  room  that  a  pane  of  glass  had  been  broken,  one 
would  straightway  set  about  finding  some  explanation  of  this 
occurrence.     One  might  perhaps  first  imagine  that  a  stone  or 

278 


§  6y.    Reasoning  from  an  Hypothesis  279 

something  of  the  kind  had  been  thrown  against  it.  Acting 
on  this  supposition,  one  would  look  for  the  stone  in  the  room. 
If  it  were  found  there,  the  hypothesis  would  be  confirmed;  if 
no  traces  of  it  could  be  discovered,  and  if,  moreover,  on  exami- 
nation the  glass  proved  to  be  shattered  in  a  way  that  would 
probably  not  result  from  the  projection  of  a  stone  against  it, 
our  first  hypothesis  would  have  to  be  abandoned.  We  should 
then  make  another  guess  —  perhaps  that  the  outside  blind 
had  been  violently  closed  by  the  wind  —  and  again  examine 
the  facts  to  see  if  they  gave  any  support  to  this  supposition. 
We  are  constantly  making  hypotheses  of  this  character  to 
explain  phenomena  which  we  meet  with  in  everyday  expe- 
rience. If  we  find  a  stream  swollen,  we  conclude  that  it  must 
have  rained  in  some  part  of  the  country  drained  by  the  stream. 
If  a  man  has  typhoid  fever,  we  are  pretty  sure  to  guess  that 
he  has  been  drinking  impure  water.  We  no  sooner  perceive 
something  unusual  or  striking  than  we  begin  to  guess  out,  as 
it  were,  its  explanation.  The  formation  of  hypotheses,  then, 
is  simply  the  mind's  response  to  the  demand  for  explanation. 
The  examples  given  above  illustrate  what  may  be  called 
the  popular,  as  opposed  to  the  scientific  use  of  hypotheses. 
In  these  cases  the  hypothesis  assumes  the  existence  of  a  par- 
ticular thing  or  event  as  that  through  which  the  phenome- 
non in  question  is  to  be  explained.  The  '  law  '  at  which  the 
induction  arrives  is  that  of  a  causal  connection  of  phenomena 
taken  in  a  descriptive  or  factual  way.  Analysis  is  not  car- 
ried on  to  reach  a  genuinely  explanatory  hypothesis,  as  it 
would  be  in  a  strictly  scientific  investigation.  Such  an 
explanatory  hypothesis  would  not  point  to  any  particular 
phenomenon  as  a  '  cause,'  but  would  state  as  a  law  certain 
permanent   forms  of  relation   in  which  things  and   events 


28c  The  Use  of  Hypotheses 

stand,  and  under  which  the  phenomenon  in  question  is 
assumed  to  fall.  Think  of  the  difference  in  character  between 
the  hypothesis  that  the  window  was  broken  by  the  slamming  of 
the  blind,  and,  for  example,  Newton's  law  of  Gravitation, 
or  the  vast  generalization  of  facts  included  in  Darwin's  law 
of  Natural  Selection. 

Nevertheless,  it  cannot  be  maintained  that  the  distinction 
is  in  any  sense  absolute  between  the  hypothesis  of  a  fact 
and  the  hypothesis  of  a  general  law  of  relation.  What  is 
an  hypothesis  at  one  stage  becomes,  when  verified,  for  fur- 
ther investigation  a  fact  or  starting  point.  Between  the 
popular  and  the  scientific  use  of  hypotheses  there  are  im- 
portant differences  of  degree,  as  has  been  pointed  out.  In 
discussing  the  use  of  hypotheses  in  this  chapter,  we  shall  have 
in  mind  primarily  the  reflective  and  critical  procedure  through 
which  certain  conceptions  are  defined  and  tested  as  instru- 
ments for  the  colligation  of  facts.  We  shall  thus  be  study- 
ing, in  its  highest  and  most  explicit  form,  the  function  that 
guides  Induction  from  its  earliest  beginnings. 

It  is  worth  noticing  that  it  is  only  unusual  or  striking 
events,  or  those  in  which  they  have  some  practical  concern, 
which  attract  the  attention  of  the  majority  of  mankind,  and 
lead  them  to  form  explanatory  hypotheses.  What  is  famil- 
iar, or  of  no  practical  importance,  does  not  usually  awaken 
curiosity.  Indeed,  in  a  great  many  cases,  such  phenomena 
are  not  observed  at  all.  But  the  great  scientist  is  distin- 
guished, one  may  say,  by  his  intellectual  curiosity.  He  tries 
to  understand  phenomena  which  the  ordinary  mind  neglects 
and  simply  takes  for  granted.  He  has  questions  in  his  mind 
with  regard  to  familiar  things  which  he  wishes  to  have  an- 
swered, guesses  which  he  is  desirous  of  having  proved  or  dis- 


§67.    Reasoning  from  an  Hypothesis  281 

proved.  Unless  the  mind  has  some  question  to  answer,  or 
theory  to  test,  it  is  impossible  to  see  any  significance  in  an 
experiment.  In  other  words,  every  experiment  must  have 
a  purpose,  and  the  purpose  is  to  get  some  information  that 
will  help  us  to  answer  a  question  which  we  bring  with  us  to 
the  investigation. 

In  the  actual  process  of  acquiring  knowledge,  then,  obser- 
vation and  theorizing  go  hand  in  hand.  Unless  we  go  to 
nature  with  something  in  our  mind,  we  are  not  likely  to  learn 
much.  As  a  rule,  we  see  only  what  we  look  for.  Francis 
Darwin  says  of  his  father:  "  He  often  said  that  no  one  could 
be  a  good  observer  unless  he  were  an  active  theorizer.  This 
brings  me  back  to  what  I  said  about  his  instinct  for  arresting 
exceptions:  It  were  as  though  he  were  charged  with  theoriz- 
ing power  ready  to  flow  into  any  channel  on  the  slightest 
disturbance,  so  that  no  fact,  however  small,  could  avoid 
releasing  a  stream  of  theory,  and  thus  the  fact  became  magni- 
fied into  importance.  In  this  way  it  naturally  happened 
that  many  untenable  theories  occurred  to  him,  but  fortu- 
nately his  richness  of  imagination  was  equalled  by  his  power 
of  judging  and  condemning  the  thoughts  which  occurred 
to  him.  He  was  just  to  his  theories  and  did  not  condemn 
them  unheard;  and  so  it  happened  that  he  was  willing  to 
test  what  would  seem  to  most  people  not  at  all  worth  testing. 
These  rather  wild  trials  he  called  '  fool's  experiments,'  and 
enjoyed  exceedingly.  As  an  example,  I  may  mention,  that 
finding  the  cotyledons  of  Biophytum  to  be  highly  sensitive 
to  vibrations  of  the  table,  he  fancied  that  they  might  perceive 
the  vibrations  of  sound,  and  therefore  made  me  play  my 
bassoon  close  to  a  plant."  l 

1  Life  and  Letters  of  Charles  Darwin,  Vol.  I.,  p.  126. 


282  The  Use  of  Hypotheses 

A  good  example  of  how  essential  theories  are  for  an 
observer,  and  how  blind  he  may  be  to  what  he  is  not  looking 
for,  is  found  in  the  work  from  which  we  have  just  quoted. 
In  the  brief  autobiography  contained  in  the  first  volume, 
Darwin  tells  of  a  geological  trip  through  Wales  which  he  took 
while  a  student  at  Cambridge,  in  company  with  Sedgwick, 
the  professor  of  geology.  It  must  be  remembered  that  this 
was  before  Agassiz  had  come  forward  with  his  theory  of  a 
glacial  period  in  the  world's  history.  Darwin  writes:  "  We 
spent  many  hours  in  Cwm  Idwal,  examining  all  the  rocks 
with  supreme  care,  as  Sedgwick  was  anxious  to  find  fossils  in 
them;  but  neither  of  us  saw  a  trace  of  the  wonderful  glacial 
phenomena  all  around  us;  we  did  not  notice  the  plainly 
scored  rocks,  the  perched  boulders,  the  lateral  and  terminal 
moraines.  Yet  these  phenomena  are  so  conspicuous  that, 
as  I  declared  in  a  paper  published  many  years  afterward  in 
the  Philosophical  Magazine,  a  house  burnt  down  by  fire  did 
not  tell  its  story  more  plainly  than  did  this  valley.  If  it 
had  been  filled  by  a  glacier,  the  phenomena  would  have  been 
less  distinct  than  they  are  now."  1 

§  68.  Formation  of  Hypotheses.  — We  are  now  ready  to 
consider  a  little  more  closely  the  formation  of  hypotheses  or 
theories.  In  the  first  place,  it  is  to  be  noticed  that  hypoth- 
eses are  not  received  from  without  through  sense-perception, 
but  are  made  by  the  mind.  They  are  the  creations  of  the 
imagination.  A  good  theorizer,  like  a  poet,  is  in  a  certain 
sense  born,  not  made.  The  man  to  whom  '  nothing  ever 
occurs,'  whose  intellectual  processes  are  never  lit  up  with  a 
spark  of  imagination,  is  unlikely  to  make  any  important  dis- 
coveries. It  has  been  by  a  flash  of  scientific  genius,  by  im- 
1  Life  and  Letters  of  Charles  Darwin,  Vol.  I.,  p.  49. 


§  68.    Formation  of  Hypotheses  283 

aginative  insight  which  we  may  almost  call  inspiration,  that 
great  scientific  theories  have  been  discovered.  Not  even  a 
scientific  genius,  however,  can  afford  to  neglect  the  facts. 
But,  guided  by  accurate  observation,  the  scientific  imagina- 
tion tries  to  invent  some  law  or  principle  which  will  serve  to 
connect  and  explain  facts.  Tyndall  has  an  essay  on  "The 
Scientific  Use  of  the  Imagination,"  from  which  we  may  quote 
a  short  passage.  "  With  accurate  experiment  and  observa- 
tion to  work  upon,  imagination  becomes  the  architect  of 
physical  theory.  Newton's  passage  from  a  falling  apple  to 
a  falling  moon  was  an  act  of  the  prepared  imagination. 
.  .  .  Out  of  the  facts  of  chemistry  the  constructive  imagina- 
tion of  Dalton  formed  the  atomic  theory.  Davy  was  richly 
endowed  with  the  imaginative  faculty,  while  with  Faraday 
its  exercise  was  incessant,  preceding,  accompanying,  and 
guiding  all  his  experiments.  His  strength  and  fertility  as  a 
discoverer  are  to  be  referred  in  great  part  to  the  stimulus  of 
the  imagination.  Scientific  men  fight  shy  of  the  word  be- 
cause of  its  ultra-scientific  connotations;  but  the  fact  is,  that 
without  the  exercise  of  this  power,  our  knowledge  of  nature 
would  be  a  mere  tabulation  of  coexistences  and  sequences."  * 

In  speaking  of  hypotheses  as  'guesses, '  or  '  creations  of  the  imagi- 
nation,' their  dependence  upon  facts  must  not  be  forgotten.  It  is 
only  when  the  phenomena  to  be  explained  have  been  carefully  ob- 
served that  our  guesses  at  their  explanation  are  likely  to  be  of  value. 
It  is  well  known  that  a  considerable  amount  of  knowledge  is  usually 
required  to  ask  an  intelligent  question.  And  in  the  same  way,  the 
mind  must  be  well  stored  with  facts,  in  order  to  render  our  hypo- 
thetical explanations  worthy  of  consideration.  Indeed,  observation 
of  facts  and  the  formation  of  theories  go  hand  in  hand,  and  natu- 

1  Fragments  of  Science,  p.  104. 


284  The  Use  of  Hypotheses 

rally  assist  each  other.  We  have  already  spoken  of  the  lack  of  theor) 
which  makes  us  blind  to  facts  that  seem  to  lie  directly  before  us. 
But  we  have  perhaps  not  yet  emphasized  sufficiently  the  dependence 
of  theories  upon  the  facts  of  observation.  The  process  of  explana- 
tion may  be  described  as  a  fitting  together  of  the  facts  given  by  ob- 
servation, with  the  explanatory  theories  which  the  mind  originates. 
The  theory  with  which  we  start  enables  us  to  ask  questions,  and 
leads  us  to  scrutinize  the  phenomena  which  are  to  be  explained ; 
while  the  latter  react  upon  the  theory,  and  cause  it  to  undergo  con- 
stant modification.  Neither  the  'theory'  nor  the  facts  are  to  be 
regarded  as  fixed  and  unchanging;  both  are  constantly  changing  in 
relation  to  each  other  as  the  investigation  proceeds.  The  account  of 
Darwin's  discovery  of  the  principle  of  'the  survival  of  the  fittest'  is 
a  good  illustration  of  an  hypothesis  constructed  by  a  constant 
dependence  upon  the  facts  during  every  step  of  its  progress. 

We  have  already  referred  to  the  way  in  which  analogy 
leads  the  mind  on  to  general  principles  of  explanation  (§  60). 
Analogy  is  a  method  of  inferring  that  what  is  true  of  one 
object  is  probably  true  of  others  which  resemble  it.  But 
the  ordinary  mind  sees  resemblances  only  when  they  are 
very  obvious  and  striking.  The  man  of  scientific  insight,  on 
the  other  hand,  like  the  poet,  penetrates  more  deeply  into  the 
nature  of  things,  and  is  able  to  discover  analogies  and  resem- 
blances to  which  the  ordinary  man  is  blind.  Who  but  a 
genius  like  Newton  would  have  thought  of  connecting  the 
fall  of  an  apple  with  the  fall  of  the  heavenly  bodies  through 
space  ?  The  history  of  science  shows  that  great  discov- 
eries are  made  by  means  of  imaginative  insight,  but  it  also 
teaches  that  mere  imagination  without  dependence  upon 
known  facts  is  frequently  a  source  of  much  mischief.  Mere 
theories  without  facts  are  not  only  empty,  but  often  stand 
in  the  way  of  true  knowledge.    The  fruitful  exercise  of  the 


§  6g.    The  Proof  of  an  Hypothesis  285 

imagination,  if  we  may  judge  from  the  way  in  which  great 
discoveries  have  been  made,  always  takes  place  in  closest 
connection  with  what  observation  and  experiment  reveal 
regarding  the  nature  of  phenomena.  If  the  imagination  is 
to  have  power  to  discover  any  truth,  it  must  constantly 
'  touch  earth,'  and  be  guided  in  its  course  by  the  nature  of 
facts  which  are  already  known. 

In  framing  hypotheses,  then,  the  imagination  is  constantly 
prompted  by  analogies  with  processes  which  are  more  or 
less  familiar.  The  hypothesis,  accordingly,  is  not  created  by 
the  imagination  '  out  of  nothing.'  It  is  rather  an  extension 
or  development  of  a  known  law,  than  an  absolute  creation. 

§  69.  The  Proof  of  an  Hypothesis.  —  We  have  discussed 
the  way  in  which  hypotheses  are  formed,  but  as  yet  have  said 
nothing  regarding  the  means  of  determining  their  truth  or 
falsity.  But  to  form  hypotheses  is  usually  easy,  to  verify 
them  is  often  exceedingly  difficult.  The  scientific  worker 
constantly  finds  that  theories  which  he  has  formed  cannot  be 
verified,  and  must  therefore  be  discarded.  It  is  not  only 
essential  that  a  scientific  investigator  shall  possess  a  mind 
fertile  in  ideas;  he  must  also  love  truth  more  than  any 
theory,  no  matter  how  interesting  or  attractive  it  may  appear. 
In  behalf  of  truth,  every  theory  must  be  subjected  to  the 
most  thorough  and  searching  tests  possible;  if  it  is  not  borne 
out  by  facts,  it  must  be  at  once  discarded.  What  now  is 
the  general  method  of  procedure  in  testing  an  hypothesis  ? 
How  do  we  proceed  to  compare  our  theories  with  the  facts  ? 
Two  steps  or  stages  may  be  distinguished  in  this  process: 
(1)  We  assume  that  the  hypothesis  is  true,  and  proceed  to 
show  what  are  the  necessary  results  which  follow  from  it. 
In  doing  this  we  proceed  deductively;   that  is,  assuming  the 


286  The  Use  of  Hypotheses 

truth  of  the  hypothesis,  we  reason  out  what  consequences 
must  follow  from  it  in  accordance  with  laws  whose  mode  of 
action  we  already  know.  (2)  The  conclusions  thus  reached 
are  compared  with  the  actual  facts,  as  given  to  us  directly 
in  perception,  or  as  determined  by  experiment.  If  they  are 
found  to  agree  with  these,  the  hypothesis  is  regarded  as  true; 
if  they  do  not  agree,  it  becomes  necessary  to  discard  the 
hypothesis,  or  to  modify  it  in  some  way  suggested  by  the  re- 
sults so  far  obtained  by  the  investigation. 

This  procedure  may  become  clearer  by  considering  some 
concrete  examples.  We  may  first  take  an  illustration  of 
what  has  been  called  the  popular  use  of  an  hypothesis.  If 
we  were  to  come  on  the  campus  some  morning  and  find  that 
several  branches  had  been  broken  from  one  of  the  trees,  we 
should  naturally  try  to  explain  this  circumstance  by  making 
some  hypothesis.  Perhaps  the  first  thing  which  would  occur 
to  us  would  be  that  there  had  been  a  violent  wind  storm. 
The  hypothesis  having  been  made,  the  next  step  would  be  to 
look  around  to  see  if  it  could  be  verified.  '  If  there  has  been 
a  cyclone,'  we  might  argue,  '  there  should  be  other  signs  of 
its  presence;  we  should  find  broken  twigs  and  blown  leaves 
lying  about,  and  all  the  trees  should  present  a  storm-tossed 
appearance.'  If  observation  showed  that  these  things  were 
actually  present,  we  would  consider  our  hypothesis  so  far 
confirmed.  But  if  not,  our  first  guess  would  be  disproved, 
and  it  would  be  necessary  to  look  about  for  another  expla- 
nation. In  this  case,  the  second  hypothesis,  being  based  on 
a  better  analysis  of  the  facts,  would  be  more  likely  to  prove 
correct  than  the  first.  But  the  process  might  have  to  be  con- 
tinued through  several  steps. 

An  excellent  illustration  of  the  way  in  which  a  scientific 


§  6g.    The  Proof  of  an  Hypothesis  287 

hypothesis  may  be  rendered  more  certain  and  at  the  same 
time  more  comprehensive  and  definite  is  found  in  the  history 
of  the  experiments  by  which  it  was  proved  that  the  atmosphere 
has  weight.  Galileo  noticed  that  water  will  rise  in  a  pump  only 
about  33  feet.  He  could  not  find  out,  however,  why  it  was  that 
the  water  stopped  at  this  point.  After  his  death,  his  friend 
and  pupil  Torricelli  took  up  the  problem,  and  asked  himself: 
Why  does  the  water  rise  at  all  ?  It  then  occurred  to  him 
that  air  must  weigh  something,  and  that  it  might  be  this 
weight  on  the  surface  of  the  water  which  forced  the  water  up 
the  pump  when  there  was  no  air  pressing  it  down.  Now,  if 
this  were  so,  he  reasoned,  the  weight  of  the  air  ought  to  lift 
mercury,  which  is  fourteen  times  heavier  than  water,  to  one- 
fourteenth  of  the  height.  So  he  took  some  mercury,  and 
filling  a  tube  about  34  inches  long,  turned  it  upside  down  into 
a  basin  of  mercury  which  was  open  and  therefore  under  the 
pressure  of  the  atmosphere.  The  mercury  began  to  settle 
in  the  tube,  and  finally  rested  at  a  height  of  30  inches.  Tor- 
ricelli had  thus  invented  the  barometer,  an  instrument  which 
would  measure  the  weight  of  the  atmosphere.  It  was  after- 
wards suggested  by  the  famous  French  writer,  Pascal,  that  at 
the  top  of  a  high  mountain,  where  there  is  less  air  pressing 
downwards,  the  column  of  mercury  should  fall  considerably 
if  the  atmosphere  were  really  what  caused  the  water  and  the 
mercury  to  rise.  When  this  experiment  was  made  by  carry- 
ing the  barometer  to  the  top  of  a  mountain  called  the  Puy  de 
Dome,  the  mercury  fell  nearly  three  inches.  Still  further 
confirmation  of  Torricelli's  theory  was  afforded  by  the  dis- 
coveries of  Otto  Guericke  of  Magdeburg.  In  1650  Guericke 
invented  the  air-pump.  The  first  use  which  he  made  of  his 
new  invention  was  to  show  that  the  atmosphere  is  pressing 


288  The  Use  of  Hypotheses 

down  upon  us  heavily  and  equally  in  all  directions.  He 
fitted  closely  together  two  metal  hemispheres  and  exhausted 
the  air  between  them  by  means  of  his  pump.  It  was  found 
that  the  pressure  of  the  atmosphere  was  so  great  that  it  took 
a  great  force  to  separate  the  hemispheres.1 

To  establish  a  scientific  theory,  then,  there  is  necessary 
not  only  a  ready  imagination,  but  also  patience  and  perse- 
verance in  the  careful  deduction  of  the  consequences  of  the 
theory,  and  in  the  comparison  of  the  results  thus  obtained 
with  the  actual  facts.  Scientific  work  also  demands  the 
utmost  candour  and  openness  of  mind  on  the  part  of  those 
who  engage  in  it.  One  must  be  willing  to  abandon  any 
theory  as  soon  as  it  is  found  to  disagree  with  the  facts.  And 
this  is  by  no  means  an  easy  thing  to  do.  When  one  has  a 
theory  which  suffices  for  nearly  all  the  facts,  there  is  always 
a  temptation  to  cling  to  it,  and  to  neglect  or  explain  away 
any  troublesome  or  contradictory  facts.  There  is  no  doubt 
that  the  scientific  explanations  which  have  become  accepted 
and  established  were  not  the  ideas  which  first  happened  to 
occur  to  the  men  with  whose  names  they  are  associated. 
When  Newton  first  attempted  to  work  out  the  verification  of 
the  gravitation  hypothesis,  he  used  the  most  accurate  meas- 
urements he  could  obtain  regarding  the  size  of  the  earth. 
But  in  calculating  on  this  basis  the  pull  of  the  earth  on  the 
moon,  and  the  consequent  deflection  of  the  moon  from  the 
straight  line,  his  results  came  out  wrong.  That  is,  the  moon 
moved  more  slowly  than  it  ought  to  move  according  to  his  theory. 
The  difference  was  not  great,  but  Newton  could  not  overlook 
this  lack  of  agreement  with  the  observed  facts.  He  put  the 
whole  matter  aside ;  and  it  was  only  when  he  heard,  sixteen 

1  Cf.  Buckley,  Short  History  of  Natural  Science,  pp.  114-121. 


§  6g.    The  Proof  of  an  Hypothesis  289 

years  later,  that  Picart  had  discovered  from  new  and  more 
accurate  measurements  that  the  earth  was  larger  than  had 
been  supposed,  that  he  repeated  his  calculations,  and  found 
his  hypothesis  verified. 

(1)  In  stating  the  general  theory  of  Induction  in  the  opening 
Chapter  (§  50),  emphasis  was  laid  on  the  part  played  by  hypotheses 
or  guiding  conceptions  from  the  very  beginning  of  an  investigation. 
Frequent  references  to  this  point  were  also  made  in  the  discussion 
of  the  various  methods.  We  learned  that  even  to  define  a  problem 
or  ask  an  intelligent  question  is  to  presume  something,  or  to  have 
some  kind  of  an  hypothesis  regarding  the  kind  of  answer  to  be 
given.  The  question  how  hypotheses  are  tested,  is  then  really  iden- 
tical with  the  question  how  inductions  in  general  are  established. 
Now,  in  explaining  and  illustrating  the  procedure  of  Induction 
and  its  use  of  the  various  methods,  attention  was  more  than  once 
directed  to  the  part  played  by  Elimination.  The  inductive  method 
of  proof,  it  was  said,  might  be  represented  by  a  Disjunctive  Syl- 
logism where  all  the  possibilities  but  one  were  eliminated  by  ex- 
hibiting their  incompatibility  with  the  facts.  But  in  these  earlier 
references  it  was  also  indicated  that  certain  qualifications  of  this 
view  are  necessary.  It  must  be  borne  in  mind  that  Elimination  is 
simply  a  means  to  an  end,  and  that  it  therefore  only  partially  de- 
scribes the  inductive  process.  The  fact  must  be  emphasized  that 
the  real  purpose  of  Induction,  as  of  all  thought,  is  to  discover  posi- 
tive connections  and  laws,  and  to  define  these  as  accurately  as 
possible. 

When  we  observe  facts  and  perform  experiments  in  order  to  test 
the  first  hypothesis  suggested  by  a  problem,  we  obtain  evidence 
which  not  merely  serves  to  eliminate  that  hypothesis,  but  which  also 
points  more  or  less  definitely  in  a  positive  direction.  It  is  not 
generally  true,  then,  that  we  approach  a  problem  with  several  defi- 
nite hypotheses  in  mind,  and  proceed  to  try  them  one  after  another 


290  The  Use  of  Hypotheses 

as  we  might  try  various  keys  at  random  in  a  lock.  But,  in  think- 
ing, as  in  all  genuine  experimentation,  failures  are  instructive. 
The  new  hypothesis  is  forged  in  and  by  the  process  of  investiga- 
tion itself,  just  as  in  the  progress  of  the  arts  finer  and  more  accurate 
instruments  are  constantly  made  possible  through  the  use  of  those 
already  in  existence.  The  Ptolemaic  theory  of  astronomy,  for  exam- 
ple, made  possible  the  observations  and  measurements  which  finally 
overthrew  it  and  gave  rise  to  the  conception  of  Copernicus.  The 
new  hypothesis,  then,  may  generally  be  better  represented  as  a 
modification  or  closer  definition  of  its  predecessor  than  as  some- 
thing quite  new  and  independent.  The  formal  representation  of 
the  Induction  by  means  of  the  Disjunctive  Syllogism,  accordingly, 
fails  to  bring  out  clearly  the  fact  of  the  development  of  knowledge 
as  the  work  of  investigation  proceeds.  And,  as  a  consequence,  the 
disjunctive  member  not  eliminated  is  represented  as  if  it  were  simply 
of  coordinate  importance  with  the  others,  and  as  if  the  fact  that  it 
was  not  eliminated  were  a  mere  accident.  Or,  put  in  other  words, 
it  fails  to  make  clear  the  fact  that  (apart  from  the  unmeaning  'in- 
finite judgment,'  e.g.  'no  good  resolution  is  an  octagon ')  all  negation 
or  elimination  has  positive  significance,  and  that  the  inductive 
analysis,  as  it  proceeds,  furnishes  positive  grounds  of  support  for 
one  hypothesis  in  and  through  the  exclusion  of  the  others.  An 
hypothesis  must  always  be  proved  by  showing  its  positive  con- 
formity with  facts :  negative  results  and  considerations  taken  alone 
never  furnish  complete  inductive  proof. 

In  dealing  with  certain  problems,  however,  or  at  certain  stages  of 
inquiry,  we  are  often  compelled  to  depend  in  large  part  on  negative 
evidence.  The  fact  that  other  hypotheses  are  excluded,  or  are  less 
satisfactory,  is  very  often  given  as  a  reason  in  support  of  a  par- 
ticular theory.  But  in  such  cases  there  always  exist,  in  addition, 
positive  reasons  in  support  of  the  theory,  though  they  are  not 
regarded  as  sufficiently  strong  to  prove  it  completely.  Moreover, 
at  a  particular  point  in  an  investigation,  we  are  sometimes  able 


§  69.    The  Proof  of  an  Hypothesis  291 

definitely  to  limit  the  number  of  possibilities.  We  do  this  in  mathe- 
matics, for  example,  when  we  say  that  one  number  or  dimension 
is  equal  to,  greater  than,  or  less  than,  another.  And  the  same  is 
sometimes  possible  in  other  fields  where  we  know  definitely  the 
exact  relations  of  things.  If  we  are  able  to  say  that  the  phenome- 
non we  are  trying  to  determine  is  either  a,  b,  or  c,we  can,  of  course, 
prove  that  it  must  be  b  by  eliminating  a  and  c.  Outside  of  mathe- 
matics, however,  the  proof  would  scarcely  ever  depend  wholly  on 
the  principle  of  Exhaustion;  but  in  eliminating  the  other  possi- 
bilities some  positive  grounds  for  the  existence  of  b  would  almost 
certainly  appear. 

(2)  The  method  of  proving  an  hypothesis  has  been  described 
(page  285  f.)  in. the  following  way : '  If  the  hypothesis  agrees  with  the 
facts  it  is  to  be  regarded  as  established ;  if  it  is  not  in  conformity 
with  them,  it  is  to  be  discarded  as  false.  Now,  when  stated  thus 
baldly,  the  professed  method  of  proof  seems  to  involve  the  fallacy 
of  affirming  the  consequent  (cf.  p.  146).  '  If  a  man  swallows 
prussic  acid  he  will  die;  he  is  dead,  and  therefore  must  have 
swallowed  the  acid. '  This  is  obviously  fallacious  reasoning.  We 
cannot  infer  that,  because  certain  facts  are  known  to  exist  which 
would  exist  if  a  certain  hypothesis  were  true,  the  hypothesis  is 
therefore  true.  When  we  speak  of  an  hypothesis  as  proved  by  its 
ability  to  explain  all  the  facts,  it  is  evident  that  some  further 
qualifications  are  necessary.  From  a  practical  point  of  view,  an 
hypothesis  is  certain  somewhat  in  proportion  to  the  number  and 
the  variety  of  the  facts  that  it  is  able  to  explain,  assuming,  of  course, 
that  there  are  no  important  relevant  facts  which  it  fails  to  explain. 
In  speaking  of  Natural  Selection,  Darwin  says :  "  This  hypothesis 
may  be  tested  ...  by  trying  whether  it  explains  several  large 
and  independent  classes  of  facts ;  such  as  the  geological  succession 
of  organic  beings,  their  distribution  in  past  and  present  times, 
and  their  mutual  affinities  and  homologies.  If  the  principle  of 
natural  selection  does  explain  these  and  other  large  bodies  of  facts 


292  The  Use  of  Hypotheses 

it  ought  to  be  received."  This  quotation  brings  out  the  fact  tha\ 
the  certainty  of  an  hypothesis  is  not  inferred  from  a  single  fact  or 
group  of  facts,  and  is  even  not  derived  from  its  agreement  with  £, 
mere  sum  of  facts.  It  is  rather  guaranteed  by  what  has  been 
well  called  the  '  Consilience  of  Results.'  An  hypothesis  is 
accepted  as  established  when  a  number  of  large  and  independent 
bodies  of  fact  all  point  toward  it  as  the  one  conception  exactly 
fitted  to  bring  them  all  into  intelligible  relations. 

From  the  standpoint  of  logic,  it  is  essential  to  prove,  not  only 
that  the  hypothesis  will  explain  the  facts,  but  that  it  is  the  only  hy- 
pothesis which  will  explain  them.  To  get  this  result,  the  other  possi- 
bilities must  obviously  be  eliminated  by  a  more  complete  and  exact 
survey  of  facts,  and  all  the  positive  circumstances  brought  to  light 
which  tend  to  confirm  the  hypothesis  in  question.  This  is  the  func- 
tion of  the '  large  and  independent  bodies  of  fact'  which  Darwin  men- 
tions in  the  passage  just  quoted.  What  is  achieved  in  this  way  is  the 
exact  fitting  together  of  facts  and  hypothesis  through  a  process  of 
progressive  adjustments.  In  the  process  the  hypothesis  is  frequently 
used  as  a  basis  for  the  prediction  of  new  facts,  which,  when  they  are 
found,  serve  in  their  turn  to  confirm  the  truth  of  the  hypothesis. 
A  most  interesting  illustration  of  this  procedure  is  afforded  by  Dar- 
win's prediction  of  the  existence  of  a  species  of  Madagascar 
moth  with  a  tongue  eleven  inches  in  length.  The  basis  of  the  pre- 
diction was  his  theory  of  the  fertilization  of  flowers  by  insects,  and 
the  adaptation  that  is  consequently  found  between  the  structure 
of  its  parts  and  certain  species  of  insects.  Shortly  after  the  ap- 
pearance of  his  book  On  Fertilization  of  Orchids  by  Insects,  a  cor- 
respondent wrote  to  him  objecting  to  the  theory  elaborated  in  that 
work:  "What  have  you  to  say  in  regard  to  an  orchid  which 
flourishes  here  in  Madagascar  possessing  a  long  nectary,  as 
slender  as  a  knitting-needle,  and  eleven  inches  in  length?  On 
your  hypothesis  there  must  be  a  moth  with  a  tongue  eleven  inches 
long,  or  this  nectary  would  never  have  been  elaborated."    Darwin 


§  70.    Requirements  of  a  Good  Hypothesis         293 

replied:1  "The  existence  of  an  orchid  with  a  slender  nectary 
eleven  inches  in  length,  and  with  nectar  secreted  at  its  tip,  is  a 
conclusive  demonstration  of  the  existence  of  a  moth  with  a  tongue 
eleven  inches  in  length,  even  though  no  such  moth  is  known." 
Not  long  afterwards  Darwin's  prediction  was  verified  by  the  dis- 
covery of  a  huge  sphinx-moth  with  a  tongue  of  the  length  pre- 
dicted. 

§  70.  Requirements  of  a  Good  Hypothesis.  — Various 
conditions  or  requisites  of  a  good  hypothesis  are  laid  down 
by  writers  on  logic.  The  three  laws  which  are  most  fre- 
quently stated  are  as  follows:  (1)  That  the  hypothesis  shall 
be  conceivable  and  not  absurd.  (2)  That  it  shall  be  of  such 
a  character  that  deductions  can  be  made  from  it.  (3)  That 
it  shall  not  contradict  any  of  the  known  laws  of  nature. 

It  does  not  seem  to  me  that  the  first  law  is  of  much  value. 
It  is  largely  individual  taste  or  education  which  leads  us  to 
pronounce  certain  theories  'absurd'  or  'inconceivable.' 
Thus,  for  a  long  time,  it  seemed  inconceivable  that  the  earth 
should  be  round,  and  should  revolve  on  its  own  axis ;  and 
less  than  a  generation  ago  the  theory  of  evolution,  as  pro- 
pounded by  Darwin,  seemed  to  many  persons  utterly '  absurd.' 
Nor  can  the  third  law  always  be  applied  as  a  test  of  an  hypoth- 
esis, for  many  great  discoveries  seemed,  at  the  time  when 

1  I  have  taken  this  story  from  W.  H.  Gibson's  Blossom  Hosts  and  Insect 
Guests  (pp.  28-29),  but  have  been  unable  to  verify  it  from  Darwin's  published 
letters.  In  the  second  edition  of  the  Fertilization  of  Orchids  (Ch.  VI.),  how- 
ever, Darwin  refers  to  this  orchid  {Angracum  sesquipedale),  and  from  the 
length  of  its  nectary  predicts  the  existence  of  a  moth  with  a  proboscis  of 
corresponding  length.  In  the  same  passage  he  goes  on  to  say:  "This  belief 
of  mine  has  been  ridiculed  by  some  entomologists,  but  we  now  know  from 
Franz  Muller  that  there  is  a  sphinx-moth  in  South  Brazil  which  has  a  pro- 
boscis of  nearly  sufficient  length,  for  when  dried,  it  was  between  ten  and 
eleven  inches  long.  When  not  protruded,  it  is  coiled  up  into  a  spiral  of  at 
least  twenty  windings"  (p.  163). 


294  The  Use  of  Hypotheses 

they  were  announced,  to  contradict  known  laws  of  nature 
The  difficulty  is  that  no  one  is  able  to  affirm,  unconditionally 
that  a  law  of  nature  forbids  us  to  make  this  or  that  hypoth- 
esis. Of  course,  we  feel  that  a  theory  is  very  probably  false 
which  is  at  variance  with  the  law  of  gravity,  or  with  that  of 
the  conservation  of  energy,  or  any  of  the  laws  which  we 
regard  as  established  beyond  a  reasonable  doubt.  But, 
although  the  chances  are  always  very  greatly  against  any 
theory  which  runs  counter  to  what  are  regarded  as  well- 
established  laws,  there  is  yet  always  a  possibility  that  it  may 
be  true.  There  is  no  law  of  nature  so  certain  as  to  be  in- 
fallible. Even  those  laws  which  appear  to  be  beyond  the 
possibility  of  doubt,  may  require  to  be  modified  or  supple- 
mented. We  may  find  that,  practically,  it  is  not  wise  to 
trouble  ourselves  with  theories  which  undertake  to  overthrow 
the  law  of  gravitation,  or  to  disprove  other  fundamental 
laws  of  the  physical  world.  But  theoretically,  at  least, 
there  is  always  a  chance  —  in  cases  such  as  we  have  been 
supposing  the  chance  is  almost  infinitely  small  —  that  the  new 
theory  may  be  right,  and  the  old  one  wrong.  The  practical 
objection  to  admitting  the  claims  of  this  canon  is  the  diffi- 
culty in  applying  it  fairly.  The  phrase,  '  contrary  to  the 
laws  of  nature,'  like  '  inconceivable,'  and  '  absurd,'  is  likely 
to  be  used  to  condemn  any  theory  with  which  one  disagrees. 
In  this  way,  it  is  evident  that  the  very  point  is  begged  which 
is  really  at  issue. 

Of  these  three  canons,  therefore,  the  second  appears  to 
state  the  only  condition  which  is  essential  to  an  hypothesis. 
An  hypothesis,  if  it  is  to  be  of  any  value,  must  be  capable  of 
being  proved  or  refuted.  But,  unless  its  consequences  can 
be  shown  by  way  of   deduction,  it  is  impossible  to  know 


§  jo.    Requirements  of  a  Good  Hypothesis  295 

whether  it  agrees,  or  does  not  agree,  with  the  facts  which  it 
is  supposed  to  explain.  An  hypothesis  from  which  nothing 
can  be  deduced,  then,  is  of  no  value  whatever.  It  always 
remains  at  the  stage  of  mere  possibility,  and  without  any  real 
connection  with  fact.  It  is  a  mere  guess  which  has  no  sig- 
nificance whatever,  for  it  is  entirely  incapable  either  of  proof 
or  of  disproof.  The  ability  of  an  hypothesis  to  lead  to  the 
prediction  of  facts  not  previously  known  to  exist  has  some- 
times been  emphasized  as  a  test  of  its  value.  But  this  cir- 
cumstance, although  making  the  hypothesis  more  impressive 
is  not  in  itself  a  proof  of  its  validity.  Indeed,  true  predic- 
tions have  frequently  been  made  on  the  basis  of  hypotheses 
which  were  afterwards  found  incorrect.  The  essential  re- 
quirement, however,  is  that  something  shall  be  deducible  from 
the  hypothesis,  that  it  shall  lead  somewhere,  and  thus  afford 
a  programme  for  further  investigation. 

(1)  In  general,  it  is  possible  to  deduce  the  consequences  of  a 
theory  only  when  the  principle  employed  is  analogous,  in  mode  of 
operation,  to  something  with  which  we  are  familiar.  Thus,  for  ex- 
ample, it  is  because  the  ether  is  conceived  as  resembling  other  mate- 
rial bodies  in  important  respects  that  it  can  be  used  as  a  principle  of 
explanation.  It  is  assumed  to  be  elastic  and  capable  of  receiving 
and  transmitting  vibrations,  and  as  spread  out  like  other  material 
bodies  in  space.  In  virtue  of  these  similarities  to  other  material 
substances,  it  is  possible  to  deduce  the  consequences  which  such 
a  substance  as  ether  would  imply,  and  to  compare  them  with  the 
actual  facts.  But  if  one  should  make  the  assumption  that  certain 
phenomena  are  due  to  some  agency  totally  unlike  anything  of  which 
we  have  any  experience,  a  disembodied  spirit,  or  ghost,  for  example, 
it  would  be  impossible  either  to  prove  or  to  disprove  the  assertion. 
For,  knowing  nothing  whatever  of  the  way  in  which  disembodied 


296  The  Use  of  Hypotheses 

spirits  act,  one  could  not  say  whether  the  phenomena  to  be  ex- 
plained, table-rapping,  planchette-writing,  etc.,  were  or  were  not 
consistent  with  a  spirit's  nature  and  habits. 

Another  example  of  a  barren  hypothesis  from  which  no  conclu- 
sions can  be  drawn,  is  afforded  by  the  'catastrophe'  or  '  convulsion ' 
theory  in  geology,  which  was  first  combated  by  Lyell,  in  his  Prin- 
ciples of  Geology,  published  in  1830.  "People  had  so  long  held  the 
belief  that  our  earth  had  only  existed  a  few  thousand  years,  that 
when  geologists  began  to  find  a  great  number  of  strange  plants  and 
animals  buried  in  the  earth's  crust,  immense  thicknesses  of  rock 
laid  down  by  water,  and  whole  mountain  masses  which  must  have 
been  poured  out  by  volcanoes,  they  could  not  believe  that  this  had 
been  done  gradually,  and  only  in  parts  of  the  world  at  a  time,  as  the 
Nile  and  the  Ganges  are  now  carrying  down  earth  to  the  sea,  and 
Vesuvius,  Etna,  and  Hecla  are  pouring  out  lava  a  few  feet  thick 
every  year.  They  still  imagined  that  in  past  ages  there  must  have 
been  mighty  convulsions  from  time  to  time,  vast  floods  swallowing 
up  plants  and  animals  several  times  since  the  world  was  made,  vio- 
lent earthquakes  and  outbursts  from  volcanoes  shaking  the  whole 
of  Europe,  forcing  up  mountains,  and  breaking  open  valleys.  It 
seemed  to  them  that  in  those  times  when  the  face  of  the  earth  was 
carved  out  into  mountains  and  valleys,  tablelands  and  deserts,  and 
when  the  rocks  were  broken,  tilted  up,  and  bent,  things  must  have 
been  very  different  from  what  they  are  now.  And  so  they  made 
imaginary  pictures  of  how  nature  had  worked,  instead  of  reasoning 
from  what  they  could  see  happening  around  them."  l 

The  convulsions,  or  catastrophes,  which  were  thus  assumed  to 
take  place  were  regarded  as  the  result  of  strange  incalculable  forces 
whose  mode  of  operation  could  never  be  exactly  determined. 
Instead  of  these  mysterious  agencies,  Lyell  assumed  that  causes 
similar  to  those  with  which  we  are  now  acquainted  had  been 
acting  uniformly  for  long  ages.     The  nature  of  the  causes  at  work 

1  Buckley,  Short  History  of  Natural  Science,  pp.  441-442. 


§  7°-    Requirements  of  a  Good  Hypothesis  297 

being  known,  it  became  possible  to  calculate  the  nature  of  the  effects, 
and  thus  to  reduce  the  facts  of  geology  to  order  and  system.  As 
we  have  already  shown,  hypotheses  which  are  to  prove  really  ser- 
viceable are  formed  by  extending  some  known  principle  through 
analogy  to  a  new  class  of  facts.  The  assumption  of  mysterious 
agencies  and  principles  whose  mode  of  operation  is  unlike  any- 
thing which  is  known  to  us,  does  not  aid  in  the  extension  of 
knowledge. 

REFERENCES 

Mill,  Logic,  Bk.  III.,  Chs.  XI.-XIV. 

W.  S.  Jevons,  The  Principles  of  Science,  Ch.  XXIII. 

C.  Sigwart,  Logic,  §  83. 

B.  Bosanquet,  Logic,  Vol.  II.,  pp.  155-167. 

L.  T.  Hobhouse,  The  Theory  of  Knowledge,  Chs.  XVII.-XIX. 

H.  W.  B  Joseph,  Logic,  Ch.  XXIII. 


CHAPTER   XX 


FALLACIES    OF   INDUCTION 


§  71.  The  Source  of  Fallacy.  —  It  is  necessary  at  the 
close  of  our  discussion  of  the  inductive  methods,  to  say 
something  regarding  the  errors  to  which  we  are  most  subject 
in  this  kind  of  thinking.  We  have  seen  that  knowledge  is  the 
result  of  the  mind's  own  activity,  and  that  it  grows  in  complete- 
ness through  a  persistent  effort  to  keep  distinct  things  which 
are  different,  and  to  connect  phenomena  which  belong  to- 
gether. Truth,  in  other  words,  is  gained  by  intellectual  activ- 
ity. And,  on  the  other  hand,  we  fall  into  error,  and  are  led 
away  by  false  arguments  as  a  result  of  mental  indolence. 
Thinking  is  hard  work,  and  there  is  always  a  tendency  to 
avoid  it.  As  a  matter  of  fact,  we  all  think  much  less  fre- 
quently than  we  suppose.  Usually,  we  are  content  to  follow 
familiar  associations,  and  to  repeat  current  phrases,  without 
doing  any  real  intellectual  work.  The  difficulty  is  that  we 
can  get  along  comfortably  without  thinking  for  the  most  part 
—  more  comfortably,  perhaps,  than  when  we  do  think. 
Then,  again,  the  mind  is  less  directly  under  control  jf  the  will 
than  the  body.  One  may  force  himself  to  sit  down  at  his 
desk  and  open  a  book;  but  it  is  more  difficult  to  compel  one- 
self to  think. 

The  only  way  in  which  we  can  be  saved  from  becoming 
'intellectual  dead-beats,'  is  by  the  formation  of  good  mental 

298 


§  72.    Fallacies  due  to  the  Careless  Use  of  Language    29c) 

habits.  It  requires  eternal  vigilance  and  unceasing  strenuous- 
ness  to  prevent  our  degeneration  into  mere  associative 
machines.  What  the  logical  doctrine  of  fallacies  can  do  is  to 
put  us  on  our  guard  against  this  tendency.  It  enumerates 
and  calls  attention  to  some  of  the  commonest  and  most  danger- 
ous results  of  slovenly  thinking,  in  the  hope  that  the  student 
may  learn  to  avoid  these  errors.  Some  of  the  fallacies  of 
which  we  shall  treat  in  this  chapter,  apply  equally  to  deductive 
or  syllogistic  reasoning,  and  have  been  already  treated  in 
Chapter  XI.  We  shall,  however,  enumerate  them  here  again 
for  the  sake  of  completeness.  It  is  convenient  to  discuss 
the  various  fallacies  under  the  following  heads:  — 

(1)  Fallacies  due  to  the  careless  use  of  Language. 

(2)  Errors  of  Observation. 

(3)  Mistakes  in  Reasoning. 

(4)  Fallacies  due  to  Individual  Prepossessions. 

After  what  has  been  said  in  the  preceding  chapters  regarding 
the  relation  of '  facts '  and  '  theories,'  it  will  not  be  supposed  that 
the  distinction  between  'errors  of  Observation'  and  'mistakes 
in  Reasoning '  is  fixed  and  absolute.  Errors  in  observation  re- 
sult frequently,  as  we  have  seen,  from  inadequate  or  confused 
conceptions.  There  is,  however,  a  relative  difference  between 
the  two  functions  of  knowledge,  which  serves  as  a  convenient 
principle  of  classification. 

§  72.  Fallacies  due  to  the  Careless  Use  of  Language. — 
The  careless  and  unreflective  use  of  words  is  a  very  frequent 
source  of  error.  Words  are  the  signs  or  symbols  of  ideas; 
but  the  natural  sluggishness  of  the  mind  leads  often  to  a  sub- 
stitution of  the  word  for  the  idea.  It  is  much  easier  to  deal 
with  counters  than  with  realities.  Since  we  must  use  words 
to  express  our  thoughts,  it  is  almost  impossible  to  prevent  them 


^00  Fallacies  of  Induction 

from  becoming  our  masters.  Bacon,  who  gives  the  name  of 
'Idols  of  the  Market-Place'  (Idolafori)  to  the  fallacies  which 
arise  through  the  use  of  words,  puts  the  matter  in  the  following 
striking  sentence:  "Men  imagine  that  their  reason  governs 
words  whilst,  in  fact,  words  react  upon  the  understanding; 
and  this  has  rendered  philosophy  and  the  sciences  sophistical 
and  inactive." '  The  dangers  connected  with  the  use  of  words 
has  also  been  well  represented  by  Locke,  from  whom  I  quote 
the  following  passage:  — 

"Men  having  been  accustomed  from  their  cradles  to  learn  words 
which  are  easily  got  and  retained,  before  they  knew  or  had  framed 
the  complex  ideas  to  which  they  were  annexed,  or  which  were  to 
be  found  in  the  things  they  were  thought  to  stand  for,  they  usually 
continue  to  do  so  all  their  lives;  and,  without  taking  the  pains  nec- 
essary to  settle  in  their  minds  determined  ideas,  they  use  their 
words  for  such  unsteady  and  confused  notions  as  they  have,  con- 
tenting themselves  with  the  same  words  other  people  use,  as  if  their 
very  sound  necessarily  carried  with  it  constantly  the  same  meaning. 
.  .  .  This  inconsistency  in  men's  words  when  they  come  to  reason 
concerning  either  their  tenets  or  interest,  manifestly  fills  their 
discourse  with  abundance  of  empty,  unintelligible  noise  and  jargon, 
especially  in  moral  matters,  where  the  words,  for  the  most  part, 
standing  for  arbitrary  and  numerous  collections  of  ideas  not  regu- 
larly and  permanently  united  in  nature,  their  bare  sounds  are  often 
only  thought  on,  or  at  least  very  obscure  and  uncertain  notions  an- 
nexed to  them.  Men  take  the  words  they  find  in  use  amongst  their 
neighbours ;  and,  that  they  may  not  seem  ignorant  what  they  stand 
for,  use  them  confidently,  without  much  troubling  their  heads  about 
a  certain  fixed  meaning ;  whereby,  besides  the  ease  of  it,  they  obtain 
this  advantage:  That,  as  in  such  discourses  they  seldom  are  in  the 
right,  so  they  are  as  seldom  to  be  convinced  that  they  are  in  the 

1  Bacon,  Novum  Organum,  Aph.  LIX. 


§  J2.    Fallacies  due  to  the  Careless  Use  of  Language    301 

wrong;  it  being  all  one  to  go  about  to  draw  those  men  out  of  then 
mistakes  who  have  no  settled  notions,  as  to  dispossess  a  vagrant  of 
his  habitation  who  has  no  settled  abode."  l 

(1)  In  treating  of  the  misuse  of  words,  we  mention,  in  the 
first  place,  errors  arising  from  the  use  of  a  word  or  phrase  in 
more  than  one  sense.  This  has  already  been  described  as 
the  fallacy  of  Equivocation.  In  some  cases,  the  equivocation 
may  be  mere  wilful  quibbling  on  the  part  of  the  person  pro- 
pounding the  argument,  as  in  the  following  example  of 
Jevons:  — 

All  criminal  actions  ought  to  be  punished  by  law, 

Prosecutions  for  theft  are  criminal  actions, 

Therefore  prosecutions  for  theft  ought  to  be  punished  by  law. 

Examples  of  this  kind  do  not  mislead  any  one;  but  in  some 
instances  the  change  of  meaning  in  words  may  not  be  per- 
ceived, even  by  the  person  who  employs  the  argument.  For 
example,  one  might  reason :  — 

It  is  right  to  do  good  to  others, 

To  assist  A  in  obtaining  office  5s  to  do  him  good, 

Therefore  it  is  right  to  assist  him  in  this  way. 

Here  the  phrase  which  is  used  equivocally  is,  'to  do  good,' 
as  will  at  once  be  perceived. 

(2)  Another  frequent  source  of  error  in  the  use  of  words 
is  found  in  what  has  been  excellently  named  the  Question- 
begging  Epithet.  As  is  well  known,  there  is  much  in  a 
name.  The  name  may  beg  the  question  directly  in  the  terms 
which  it  applies,  or  it  may  arouse  misleading  associations. 
Epithets,   like  'class-legislation,'   'compromise  measure,'  'a 

1  Essay  Concerning  Human  Understanding,  Bk.  III.,  Ch.  X. 


302  Fallacies  of  Induction 

dangerous  and  immoral  doctrine,'  are  terms  freely  used  to 
describe  the  measures  or  views  of  opponents.  And,  as  it  is 
always  easier  to  adopt  a  current  phrase,  than  to  examine  the 
facts  and  draw  our  own  conclusions,  it  is  not  surprising  that 
the  name  settles  the  whole  matter  in  the  minds  of  so  many 
people.  Of  course,  the  epithet  employed  may  beg  the  ques- 
tion in  favour  of  the  subject  it  is  used  to  describe,  as  well  as 
against  it.  Politicians  well  understand  the  importance  of 
adopting  an  impressive  and  sonorous  election  cry  to  represent 
the  plank  of  their  party.  Thus,  party  cries  like  'honest 
money,'  'prohibition  and  prosperity,'  'the  people's  cause,' 
etc.,  are  essentially  question-begging  epithets.  Even  words 
like  'liberty,'  'justice,'  and  'patriotism,'  are  frequently  used 
in  such  a  way  as  to  bring  them  under  the  class  of  fallacies 
which  we  have  here  described.  Under  this  heading,  also, 
may  be  grouped  'cant'  words  and  phrases.  When  we  accuse 
a  person  of  using  cant,  we  always  imply  that  he  is  more  or  less 
consciously  insincere,  that  he  is  professing  opinions  and  senti- 
ments which  he  does  not  really  possess.  Any  insincere  ex- 
pression which  is  made  primarily  for  the  sake  of  effect  may 
be  rightly  termed  cant.  It  is  not  even  necessary  that  the 
speaker  should  bs  fully  conscious  of  his  insincerity.  A  man 
may  easily  deceive  himself,  and,  as  he  repeats  familiar  words 
and  phrases,  imagine  himself  to  be  overflowing  with  patriotism, 
or  with  sympathy  for  others,  or  with  religious  feelings. 

(3)  Figurative  language  is  another  frequent  source  of 
error.  Of  the  various  figures  of  speech,  perhaps  metaphors 
are  the  most  misleading.  The  imagery  aroused  by  metaphori- 
cal language  is  usually  so  strong  as  to  make  us  forget  the 
difference  between  the  real  subject  under  consideration  and 
the  matter  which  has  been  used  to  illustrate  it.     Thus,  in 


§  73-    Errors  of  Observation  303 

discussing  problems  of  mind,  it  is  very  common  to  emplo5 
metaphors  drawn  from  the  physical  sciences.     For  example, 
we  read  in  works  on  psychology  and  ethics  of  'the  struggle 
of  ideas,'  of  'the  balancing  and  equilibration  of  motives,'  of 
'  action  in  the  direction  of  the  strongest  motive,'  etc.     Another 
illustration,  which  has  been  often  quoted,  is  Carlyle's  argu- 
ment   against    representative   government   founded    on   the 
analogy  between  the  ruler  of  a  state  and  the  captain  of  a  ship. 
The  captain,  he  says,  could  never  bring  the  ship  to  port  if  it 
were  necessary  for  him  to  call  the  crew  together,  and  get  a 
vote  every  time  he  wished  to  change  the  course.    The  real 
difference  between  the  relation  of  a  captain  to  his  crew,  and 
the  executive  officers  in  a  state  to  the  citizens,  is  lost  sight  of 
by  the  metaphor.    Metaphors  should  be  used  only  to  illus- 
trate and  suggest,  and  never  to  prove.    Metaphorical  reason- 
ing is  simply  a  case  of  analogy,  the  imperfections  and  dangers 
of  which  have  been  already  pointed  out.     It  is,  however, 
one  of  the  errors  which  it  is  most  difficult  to  avoid.     A  hidden 
metaphor  lurks  unsuspected  in  many  of  the  words  in  common 
use.     We  may  thus  appreciate  the  force  of  Heine's  humorous 
petition:  "May  Heaven  deliver  us  from  the  Evil  One,  and 
from  metaphors."  l     It  is,  of  course,  not  necessary  or  desir- 
able to  abstain  entirely  from  the  use  of  metaphors.     What  is 
essential  is  to  prevent  them  from  '  reacting  upon  the  understand- 
ing.'    A  person  who  is  able  to  employ  many  metaphors  drawn 
from  various  fields  is  perhaps  less  likely  to  be  misled  by 
them,  than  the  unimaginative  man — the  man  of  one  figure 
and  one  phrase  —  whose  mind  sticks  in  mechanical  grooves. 
§   73.    Errors    of     Observation.  —  Sometimes    insufficient 
observation  is  the  result  of  a  previously  conceived  theory; 

'  Quoted  by  Minto,  Logic,  p.  373. 


304  Fallacies  of  Induction 

sometimes  it  may  be  due  to  inattention,  to  the  difficulties  of 
the  case,  or  to  lack  of  the  proper  instruments  and  aids  to 
observation.  We  have  already  had  occasion  to  refer  to  the 
influence  of  a  theory  on  observation  (cf.  §  67).  As  a  rule, 
we  see  only  those  instances  which  are  favourable  to  the 
theory  or  belief  which  we  already  possess.  It  requires  a 
special  effort  of  attention  to  take  account  of  negative  instances, 
and  to  discover  the  falsity  involved  in  some  long-standing 
belief.  Indeed,  it  perhaps  requires  quite  as  much  mental  alert- 
ness to  overthrow  an  old  theory,  as  to  establish  a  new  one. 
It  is  obvious  that  the  fallacy  here  is  due,  as  is  generally  the 
case,  to  insufficient  observation  and  analysis.  The  conclusion 
is  based  on  an  uncritical  use  of  the  method  of  Agreement, 
without  any  attempt  to  compare  the  positive  cases  with  in- 
stances where  the  phenomenon  is  absent.  This  comparison  is 
made  by  the  method  of  Difference.  This  tendency  of  the 
mind  to  seize  upon  affirmative  instances,  and  to  neglect  the 
evidence  afforded  by  negative  cases,  is  well  set  forth  by  Bacon 
in  the  following  passage:  — 

"The  human  understanding,  when  any  proposition  has  been 
once  laid  down  (either  from  general  admission  and  belief,  or  from 
the  pleasure  it  affords),  forces  everything  else  to  add  fresh  support 
and  confirmation;  and  although  most  cogent  and  abundant  in- 
stances may  exist  to  the  contrary,  yet  either  does  not  observe  or 
despises  them,  or  gets  rid  of  and  rejects  them  by  some  distinction, 
with  violent  and  injurious  prejudice,  rather  than  sacrifice  the  au- 
thority of  its  first  conclusions.  It  was  well  answered  by  him  who 
was  shown  in  a  temple  the  votive  tablets  suspended  by  such  as  had 
escaped  the  peril  of  shipwreck,  and  was  pressed  as  to  whether  he 
would  then  recognize  the  power  of  the  gods;  'But  where  are  the 
portraits  of  those  who  have  perished  in  spite  of  their  vows?'  All 
superstition  is  much  the  same,  whether  it  be  that  of  astrology, 


§  73-    Errors  of  Observation  305 

dreams,  omens,  retributive  judgment,  or  the  like,  in  all  of  which  the 
deluded  observers  observe  events  which  are  fulfilled,  but  neglect 
and  pass  over  their  failure,  though  it  be  much  more  common.  But 
this  evil  insinuates  itself  still  more  craftily  in  philosophy  and  the 
sciences,  in  which  a  settled  maxim  vitiates  and  governs  every  other 
circumstance,  though  the  latter  be  much  more  worthy  of  confidence. 
Besides,  even  in  the  absence  of  that  eagerness  and  want  of  thought 
(which  we  have  mentioned),  it  is  the  peculiar  and  perpetual  error  of 
the  human  understanding  to  be  more  moved  and  excited  by  affirma- 
tives than  negatives,  whereas  it  ought  duly  and  regularly  to  be  im- 
partial ;  nay,  in  establishing  any  true  axiom  the  negative  instance  is 
the  most  powerful."  l 

The  nature  of  this  fallacy  has  been  so  well  illustrated 
by  the  quotation  which  has  just  been  given,  that  we  may 
pass  on  at  once  to  speak  of  other  cases  of  insufficient  observa- 
tion. Our  discussion  of  the  processes  of  reasoning  have  made 
it  clear  how  necessary  it  is  to  observe  carefully  and  attentively. 
The  majority  of  the  false  theories  which  have  appeared  in 
science  and  in  philosophy,  as  well  as  those  of  common  life, 
have  arisen  from  lack  of  observation.  The  doctrine  of  innate 
ideas,  and  the  theory  that  combustion  was  a  process  of  giving 
off  phlogiston  —  a  substance  supposed  to  be  contained  in 
certain  bodies  —may  be  given  as  examples.  With  regard  to 
phlogiston,  Mill  says:  "The  hypothesis  accorded  tolerably 
well  with  superficial  appearances :  the  ascent  of  flame  naturally 
suggests  the  escape  of  a  substance;  and  the  visible  residuum 
of  ashes,  in  bulk  and  weight,  generally  falls  extremely  short 
of  the  combustible  material.  The  error  was  non-observation 
of  an  important  portion  of  the  actual  residue;  namely,  the 
gaseous  products  of  combustion.  When  these  were  at  last 
noticed  and  brought  into  account,  it  appeared  to  be  a  universal 

1 Novum  Organum,  Bk.  I.,  Aph.  XLVI. 


306  Fallacies  of  Induction 

law  that  all  substances  gain  instead  of  losing  weight  by  com- 
bustion; and  after  the  usual  attempt  to  accommodate  the  old 
theory  to  the  new  fact  by  means  of  an  arbitrary  hypothesis 
(that  phlogiston  had  the  quality  of  positive  levity  instead  of 
gravity),  chemists  were  conducted  to  the  true  explanation, 
namely,  that  instead  of  a  substance  separated,  there  was,  on 
the  contrary,  a  substance  absorbed."1  This  illustration  also 
exemplifies  the  consequences  both  of  neglecting  Residues  and 
of  noticing  and  seeking  to  explain  them.  In  some  seaside 
communities,  there  is  a  belief  that  living  beings,  both  human 
and  animal,  never  die  at  flood  tide.  '  They  always  go  out 
with  the  ebb,'  it  is  said.  Again,  there  is  a  general  belief, 
which  was  shared  by  such  an  eminent  scientist  as  Herschel, 
that  the  full  moon  in  rising  possesses  some  power  of  dispersing 
the  clouds.  Careful  observations  made  at  the  Greenwich  ob- 
servatory have,  however,  shown  conclusively  that  the  moon 
has  no  such  power  as  that  supposed.2 

Another  circumstance  to  be  considered  in  this  connection  is 
the  inaccuracy  and  fallibility  of  ordinary  memory.  Every  one 
must  have  noticed  how  rarely  two  persons  agree  completely 
in  the  report  which  they  give  of  a  conversation  which  they 
have  heard,  or  of  events  which  they  have  experienced.  This 
is  due  in  part  to  diversity  of  interest:  each  person  remembers 
those  circumstances  in  which  for  any  reason  he  is  most  strongly 
interested.  But,  in  addition,  it  is  largely  the  result  of  the  in- 
evitable tendency  of  the  mind  to  confuse  what  is  actually 
observed,  with  inferences  made  from  its  observations.  The 
inability  to  distinguish  between  what  is  really  perceived,  and 
what   is  inferred,   is  most  strongly  marked  in  uneducated 

1  Logic,  Bk.  V.,  Ch.  IV. 

2  Cf.  Jevons,  Principles  of  Science,  Ch.  XVIII. 


§  7 '3-    Errors  of  Observation  307 

persons,  who  are  not  on  their  guard  against  this  fallacy. 
An  uneducated  person  is  certain  to  relate,  not  what  he  actually 
saw  or  heard,  but  the  impression  which  the  events  experienced 
made  upon  him.  He  therefore  mixes  up  the  facts  perceived, 
with  his  own  conclusions  drawn  from  them,  and  with  state- 
ments of  his  own  feelings  in  the  circumstances.  A  lawyer  who 
has  to  cross-examine  a  witness  is  usually  well  aware  of  this 
tendency,  and  takes  advantage  of  it  to  discredit  the  testimony. 
The  experienced  physician  knows  how  worthless  is  the  descrip- 
tion of  symptoms  given  by  the  ordinary  patient,  or  by  sympa- 
thetic friends,  or  by  an  inexperienced  nurse.  The  more 
one's  sympathies  and  interests  are  aroused  in  such  a  case,  the 
more  difficult  it  is  to  limit  oneself  to  an  exact  statement  of 
actual  occurrences. 

But  this  tendency  is  not  confined  to  persons  deficient  in 
knowledge  and  ordinary  culture.  It  usually  requires  special 
training  to  make  one  a  good  observer  in  any  particular  field. 
It  is  by  no  means  so  easy  as  it  may  appear  to  describe  exactly 
what  one  has  seen  in  an  experiment.  If  we  know,  or  think 
that  we  know,  the  explanation  of  the  fact,  there  is  an  almost 
inevitable  tendency  to  substitute  this  interpretation  for  the 
account  of  what  has  been  actually  observed.  Recent  psy- 
chological investigation,  aided  by  exact  experimental  methods, 
has  done  much  to  disentangle  the  data  of  perception  from 
inferences  regarding  these  data.  As  every  one  knows  who 
has  practised  psychological  introspection,  it  is  only  with  the 
utmost  difficulty,  and  after  long  training,  that  one  can  distin- 
guish the  actual  psychological  processes  present  to  conscious- 
ness, from  the  associative  and  logical  elements  which  are 
bound  up  with  them  in  our  ordinary  experience.  The  follow- 
ing passage  from  Mill  deals  with  this  question:  — 


308  Fallacies  of  Induction 

"The  universality  of  the  confusion  betveen  perceptions  and  the 
inferences  drawn  from  them,  and  the  rarity  of  the  power  to  discrimi* 
nate  the  one  from  the  other,  ceases  to  surprise  us  when  we  consider 
that  in  the  far  greater  number  of  instances  the  actual  perceptions  of 
our  senses  are  of  no  importance  or  interest  to  us  except  as  marks 
from  which  we  infer  something  beyond  them.  It  is  not  the  colour 
and  superficial  extension  perceived  by  the  eye  that  are  important  to 
us,  but  the  object  of  which  these  visible  appearances  testify  the 
presence ;  and  where  the  sensation  itself  is  indifferent,  as  it  gener- 
ally is,  we  have  no  motive  to  attend  particularly  to  it,  but  acquire  a 
habit  of  passing  it  over  without  distinct  consciousness,  and  going  on 
at  once  to  the  inference.  So  that  to  know  what  the  sensation  ac- 
tually was  is  a  study  in  itself,  to  which  painters,  for  example,  have 
to  train  themselves  by  long-continued  study  and  application.  In 
things  further  removed  from  the  dominion  of  the  outward  senses, 
no  one  who  has  not  had  great  experience  in  psychological  analysis 
is  competent  to  break  this  intense  association ;  and  when  such  ana- 
lytic habits  do  not  exist  in  the  requisite  degree,  it  is  hardly  possible 
to  mention  any  of  the  habitual  judgments  of  mankind  on  sub- 
jects of  a  high  degree  of  abstraction,  from  the  being  of  God  and 
the  immortality  of  the  soul  down  to  the  multiplication  table,  which 
are  not,  or  have  not  been,  considered  as  matter  of  direct  intuition. "  * 

(i)  In  pointing  out  the  evils  arising  from  confusing  fact 
and  theory,  it  is  not  forgotten  that  what  are  taken  as  '  facts ' 
are  the  results  of  earlier  theorizings  and  interpretations  (cf. 
§  53).  But  the  results  of  past  processes  of  combination  and 
comparison  become  embodied  or  fixed  in  more  or  less  definite 
form  in  the  course  of  experience.  Moreover,  they  are  fixed 
in  language  —  whether  in  the  language  of  common  life  or  in 
the  technical  terminology  of  the  different  sciences.  There 
always  is  a  kind  of  convention  conveyed,  both  by  the  lan- 

1  Logic,  Bk.  V.,  Ch.  IV.,  §  5, 


§  74-    Mistakes  in  Reasoning  309 

guage  of  ordinary  life  and  by  that  of  the  sciences  as  to  what 
may  be  taken  as  a  fact  in  that  court  circle,  —  i.e.  taken  for 
granted  as  a  datum  or  starting-point  for  further  construc- 
tion. What  is  a  fact  in  science  may,  of  course,  be  an  infer- 
ence from  the  standpoint  of  popular  knowledge,  or  vice 
versa. 

Now,  the  fallacy  against  which  warning  is  here  given,  arises 
from  not  understanding  clearly  what,  in  any  given  circum- 
stance, may  properly  be  taken  as  '  fact.'  If  there  is  confusion 
as  to  the  starting-point,  there  is  no  proper  basis  on  which 
to  construct  a  theory.  Moreover,  without  some  certain 
starting-point,  some  well-ascertained  datum,  there  is  no 
means  of  testing  and  criticising  our  theories. 

§  74.  Mistakes  in  Reasoning.  — The  problem  of  the  induc- 
tive processes  of  reasoning  is  to  ascertain  what  facts  are  neces- 
sarily and  essentially  connected,  and  to  explain  thisconnection. 
Now,  in  order  to  distinguish  between  chance  conjunctions  of 
phenomena,  and  real  causal  connections,  careful  and  extensive 
observation,  aided  whenever  possible  by  experiment,  must  be 
employed.  In  short,  to  establish  a  real  law  of  connection 
between  phenomena,  it  is  necessary  to  use  one  or  more  of  the 
inductive  methods  described  in  Chapters  XVI.  and  XVII. 
But  to  do  this  implies,  in  many  cases,  long  processes  of  analy- 
sis; the  performance  of  intellectual  work,  which  ordinary 
minds,  at  least,  have  the  tendency  to  shirk  whenever  possible. 
It  is  much  easier  to  allow  associations  to  control  our  thoughts, 
and  to  assume,  (1)  that  events  which  happen  together  in  our 
experience  a  number  of  times  are  causally  connected;  or, 
(2)  that  things  that  are  in  some  way  alike  are  causally  con- 
nected, or  of  the  same  kind.  We  are  led  to  such  a  conclusion 
by  a  natural  psychological  tendency,  without  taking  any 


3 10  Fallacies  of  Induction 

thought  about  the  matter,  while  logical  analysis  and  discrimi- 
nation  require  a  distinct  conscious  effort. 

The  general  name  used  to  describe  the  first  class  of  fallacies 
which  are  due  to  this  particular  form  of  mental  sluggishness 
is  post  hoc,  ergo  propter  hoc.  Two  events  occur  in  close  con- 
junction with  each  other,  and  it  is  then  assumed  without 
further  investigation  that  they  are  related  to  each  other  as 
cause  and  effect.  Many  popular  superstitions  are  examples 
of  this  fallacy.  Some  project  begun  on  Friday  turns  out  dis- 
astrously, and  it  is  inferred  that  some  causal  relation  existed 
between  the  fate  of  the  enterprise,  and  the  day  on  which  it 
was  begun.  Or  thirteen  persons  sit  down  to  dinner  together, 
and  some  one  dies  before  the  year  is  out.  It  is  to  be  noticed 
that  such  beliefs  are  supported  by  the  tendency,  to  which  we 
referred  in  the  last  section,  to  observe  only  the  instances  in 
which  the  supposed  effect  follows,  and  to  neglect  the  negative 
cases,  or  cases  of  failure.  'Fortune  favours  fools,'  we  exclaim 
when  we  hear  of  any  piece  of  good  luck  happening  to  any  one 
not  noted  for  his  wisdom.  But  we  fail  to  take  account  of  the 
more  usual  fate  of  the  weak-minded.  The  belief  that  the 
full  moon  in  rising  disperses  the  clouds,  which  was  also 
quoted  earlier,  is  a  good  example  of  post  hoc,  propter  hoc. 
In  fact,  all  the  fallacies  treated  in  this  chapter,  except  those 
due  to  language,  might  quite  properly  be  included  under 
this  heading.  The  tendency  to  neglect  negative  instances 
was  given  by  Bacon  as  the  most  striking  example  of  the  '  Idols 
of  the  Tribe'  (Idola  tribus),  i.e.  of  the  species  of  fallacies  to 
which  the  whole  tribe  or  race  of  men  are  subject. 

A  special  case  of  this  fallacy,  to  which  attention  may  be 
called  separately,  arises  from  hasty  generalization,  or  generali- 
zation on  an  insufficient  basis  of  fact.    The  term  '  generalize 


§  74-    Mistakes  in  Reasoning  311 

tion'  is  often  used  in  logic  to  denote  the  whole  inductive  move- 
ment of  thought  from  particular  facts  to  general  principles 
and  laws.  But  the  fallacy  to  which  reference  is  here  made 
usually  concerns  a  special  stage  in  that  process — the  stage 
where  a  first  generalization  is  made  from  instances.  We 
are  said  to  generalize  when,  after  a  more  or  less  extended  anc 
careful  set  of  observations,  we  take  the  instances  observed  as 
typical  of  all  phenomena  of  the  same  field,  or  of  the  same 
general  character.  When  due  care  has  not  been  exercised 
in  making  the  observations  or  when  the  observations  are  few 
in  number,  or  all  drawn  from  a  limited  part  of  the  whole 
field,  we  speak  of  '  hasty  generalization.'  Thus  it  is  not  un- 
usual to  hear  a  traveler  declare,  on  the  basis  of  a  very  limited 
experience,  that  '  the  hotels  of  some  city  or  country  are 
thoroughly  bad.'  The  generalizations  which  are  so  fre- 
quently made  regarding  the  peculiar  characteristics  of  Ameri- 
cans, or  Englishmen,  or  Frenchmen  are  usually  of  the  same 
sort.  Conclusions  regarding  the  effect  of  moral  and  political 
conditions,  too,  are  often  drawn  from  observations  in  a  limited 
field.  Even  scientific  books  are  not  always  free  from  this 
error.  In  a  recently  published  psychological  study  of  the 
first  year  of  the  life  of  a  child,  by  the  mother,  it  was  explained 
why  a  baby  always  sucks  its  thumb  rather  than  its  fingers. 
The  explanation  was  that  the  thumb,  being  on  the  outside  and 
projecting  outwards,  got  oftenest  into  the  baby's  mouth, 
and  so  the  habit  was  formed.  The  point  is,  that  the  mother 
assumed  what  she  had  observed  in  her  own  child  to  be  true 
universally.  Other  parents,  however,  declare  that  their 
babies  never  put  the  thumb  into  the  mouth,  but  always  the 
fingers  or  the  whole  hand. 
Another  fallacy  belonging  to  this  group  arises  from  the 


3 1 2  Fallacies  of  Induction 

uncritical  use  of  Analogy.  False  Analogy  is  closely  connected 
with  the  fallacies  of  figurative  language.  Indeed,  the  latter  type 
of  fallacies,  almost  without  exception,  arise  from  a  loose  use  of 
Analogy.  It  has  been  pointed  out  (§  66),  that  the  value  of 
an  inference  from  Analogy  depends  upon  the  'depth'  or  'im- 
portance' of  the  resemblances  upon  which  it  is  based.  False 
inferences  arise  in  every  field  from  taking  some  striking  or 
surface  resemblance  as  the  basis  of  a  conclusion.  Nothing 
is  easier  than  to  be  led  uncritically  by  vague  resemblances,  or 
even  to  imagine  them  where  they  do  not  exist.  Vague  or 
fancied  analogies  are  the  foundation  of  many  popular  super- 
stitions regarding  omens,  illness,  cures,  etc.,  and  also  play 
an  important  part  in  many  of  the  sympathetic  and  imita- 
tive practices  of  Magic. 

§  75.  Fallacies  due  to  Individual  Prepossessions.  — Bacon 
named  this  class  of  fallacy  "  The  Idols  of  the  Cave."  Each 
individual,  as  he  represents  the  matter,  is  shut  up  in  his  own 
cave  or  den;  that  is,  he  judges  of  things  from  his  own  individ- 
ual point  of  view.  In  the  first  place,  one's  inclinations  and 
passions,  likes  and  dislikes,  pervert  one's  judgment.  It  is 
exceedingly  difficult,  as  we  all  know,  to  be  fair  to  a  person 
we  dislike,  or  to  refrain  from  judging  too  leniently  the  short- 
comings of  those  to  whom  we  are  warmly  attached.  Again, 
it  is  not  easy  to  put  oneself  in  the  position  of  an  impartial 
spectator  when  one's  interests  are  at  stake.  "The  under- 
standing of  men,"  says  Bacon,  "  resembles  not  a  dry  light,  but 
admits  some  tincture  of  the  passions  and  will."  Furthermore, 
each  individual  has  a  certain  personal  bias  as  a  result  of  his 
natural  disposition  and  previous  training.  Thus  it  is  almost 
impossible  for  an  individual  to  free  himself  from  national 
prejudices,  or  from  the  standpoint  of  the  political  party,  or  the 


§  75-    Fallacies  due  to  Individual  Prepossessions      313 

church  in  which  he  was  brought  up.  Or,  if  a  person  does 
give  up  his  old  views,  he  not  infrequently  is  carried  to  the 
opposite  extreme,  and  can  see  no  good  in  what  he  formerly 
believed.  Even  education  and  the  pursuit  of  special  lines  of 
investigation  may  beget  prejudices  in  favour  of  particular  sub- 
jects. When  a  man  has  been  engaged  exclusively  for  a  long 
time  in  a  particular  field,  employing  a  particular  set  of  con- 
ceptions, it  is  almost  inevitable  that  he  should  look  at  every- 
thing with  which  he  has  to  do  in  the  same  light.  The  mathe- 
matician's view  of  the  world  is  almost  sure  to  be  different 
from  that  of  the  historian,  or  that  of  the  student  of  aesthetics. 
It  is  very  difficult  for  the  physicist  to  conceive  of  any  natural 
process  except  in  terms  of  molecules  and  vibrations.  It  is 
inevitable  that  each  man  should  be  blinded  to  some  extent 
by  his  own  presuppositions.  But  to  recognize  one's  limi- 
tations in  this  respect,  is  to  pass,  to  some  extent  at  least, 
beyond  them. 

(1)  Moreover,  each  age,  as  well  as  each  individual,  may  be  re- 
garded as  governed  largely  by  current  presuppositions  and  preju- 
dices. Bacon  does  not,  however,  classify  the  errors  into  which 
one  may  be  led  by  the  spirit  of  the  time  (Zeitgeist),  or  the  beliefs 
derived  from  the  past,  with  the  'Idols  of  the  Cave,'  but  speaks 
of  them  rather  as  "  Idols  of  the  Theatre."  {I dola  theatri) .  He 
draws  his  examples  of  this  from  the  influence  which  the  traditions 
of  the  Schoolmen  still  continued  to  exert  in  his  own  day. 
Throughout  the  Middle  Ages,  theological  doctrines  and  opinions 
controlled  almost  absolutely  the  opinions  and  beliefs  of  man- 
kind. This  influence,  doubtless,  still  makes  itself  felt,  but  people 
are  now  pretty  generally  awake  to  the  dangers  from  this  source. 
On  the  other  hand,  it  is  more  difficult  to  realize  at  the  present 
time  that  it  is  not  impossible  for  prejudices  and  prepossessions 


314  Fallacies  of  Induction 

to  grow  out  of  scientific  work.  The  success  of  modern  scientific 
methods  has  sometimes  led  investigators  to  despise  and  belittle 
the  work  of  those  who  do  not  carry  on  their  investigations  in 
laboratories,  or  do  not  weigh  and  measure  everything.  But  con- 
ceptions and  methods  which  prove  useful  in  one  science  cannot 
always  be  employed  profitably  in  another.  A  conception,  or 
mode  of  regarding  things,  which  has  proved  serviceable  in  one 
field  is  almost  certain  to  dominate  a  whole  age,  and  to  be  used  as 
an  almost  universal  principle  of  explanation.  The  eighteenth 
century,  for  example,  was  greatly  under  the  influence  of  mechanical 
ideas.  Newton's  discovery  made  it  possible  to  regard  the  world 
as  a  great  machine,  the  parts  of  which  were  all  fitted  together 
according  to  the  laws  of  mechanics.  This  view  led  to  such  a 
vast  extension  of  knowledge  in  the  realm  of  physics  and  astron- 
omy, that  the  conceptions  upon  which  it  is  based  were  applied 
in  every  possible  field  —  in  psychology,  in  ethics,  in  political 
science.  The  world  itself,  as  well  as  religious  creeds  and  political 
and  social  institutions,  were  supposed  to  have  been  deliberately 
made  and  fashioned  by  some  agent.  Again,  at  the  present  time 
we  are  dominated  by  the  idea  of  evolution.  The  biological  notion 
of  an  organism  which  grows  or  develops  has  been  applied  in  every 
possible  field.  We  speak,  for  example,  of  the  world  as  an  organ- 
ism rather  than  as  a  machine,  of  the  state  and  of  society  as  organic. 
And  the  same  conception  has  been  found  useful  in  explaining  the 
nature  of  human  intelligence.  It  is  easy  for  us  to  realize  the 
limitations  and  insufficiency  of  the  notion  of  mechanism  as  em- 
ployed by  the  thinkers  of  the  eighteenth  century.  But  it  is  not 
improbable  that  a  future  century  may  be  able  to  see  more 
clearly  than  we  are  able  to  do,  the  weaknesses  and  limi- 
tations of  the  conception  which  has  proved  so  fruitful  in  this 
generation. 


§75-    Fallacies  due  to  Individual  Prepossessions      315 

REFERENCES 

Bacon,  Novum  Organum,  Aph.  XXX VIII. -LXVIII. 
Locke,  Essay  Concerning  Human  Understanding,  Bk.  III.,  Chs.  X 
and  XL 

J.  S.  Mill,  Logic,  Bk.  V. 

A.  Bain,  Logic,  Pt.  II.,  Induction,  Bk.  VI. 

J.  Fowler,  Inductive  Logic,  Ch.  VI. 

J.  G.  Hibben,  Inductive  Logic,  Ch.  XVII. 

A.  Sidgwick,  Fallacies  [Int.  Scient.  Series]. 


PART  III.  — THE  NATURE  OF 
THOUGHT 

CHAPTER  XXI 

JUDGMENT  AS  THE  ELEMENTARY  PROCESS  OF  THOUGHT 

§  76.    Thinking  the  Process   by  which  Knowledge  grows 

or  Develops. — Logic  was  defined  (§  1)  as  the  science  of 
thinking,  and  we  have  seen  that  the  business  of  thought 
is  to  furnish  the  mind  with  truth  or  knowledge.  Under 
what  general  conception,  now,  shall  we  bring  thinking, 
and  what  method  shall  we  adopt  to  aid  us  in  its  investi- 
gation? It  is  at  once  clear  that  thinking,  the  conscious 
process  by  which  knowledge  is  built  up,  does  not  resemble 
mechanical  processes  like  pressure,  or  attraction  and  re- 
pulsion. It  is  more  nearly  related  to  something  which  has 
life,  like  a  plant  or  an  animal,  and  which  grows  or  develops 
from  within,  in  accordance  with  the  laws  of  its  own  nature. 
Thinking  must  be  regarded  rather  as  a  living  process,  than 
as  a  dead  thing,  though  it  is  necessary  also  to  remember 
that  it  is  conscious  as  well  as  living. 

When  the  thinking  process  is  regarded  in  this  way,  more- 
over, a  method  of  procedure  at  once  suggests  itself.  In 
these  days  we  have  become  familiar  with  the  notion  of  evolu- 
tion or  development,  and  the  application  of  this  notion  has 
proved  of  the  greatest  service  to  science,  and  particularly 
to  those  sciences  which  deal  with  the  phenomena  of  life. 
What  is  characteristic  of  this  manner  of  regarding  things 

316 


\  7J.    Lazv  of  Evolution  and  its  Application  to  Logic     317 

is  the  fact  that  it  does  not  consider  the  various  phenomena 
with   which    it  deals   as   fixed,   unchangeable   things,   each 
with  a  ready-made  nature  of  its  own.     But  each  thing  is 
simply  a  stage  of  a  process,  a  step  on  the  way  to  something 
else.     And  the  relations  of  the  various  phenomena  to  each 
other,  their  connection  and  unity  as  parts  of  the  one  process, 
come  out  more  clearly  when  viewed  in  this  way.     In  other 
words,  by  taking  a  survey  of  the  genesis  and  growth  of 
things,  or  the  way  in  which  they  come  to  be,  we  gain  a  truer 
idea  of  their  nature  and  relations  than  would  be  possible 
in  any  other  way.    The  past  history  of  any  phenomenon, 
the  story  of  how  it  came  to  be  what  it  is,  is  of  the  greatest 
possible  service  in  throwing  light  upon  its  real  nature.    Now, 
one  cannot  doubt  that  this  conception  will  also  prove  ser- 
viceable in  the  study  of  logic.    That  is  to  say,  it  will  assist 
us  in  gaining  a  clearer  idea  of  the  nature  of  thinking,  to  con- 
ceive it  as  a  conscious   function,  or  mode  of   acting,  which 
unfolds  or  develops  in  accordance  with  the  general  laws  of 
organic    evolution.     And    this    process    may    be    supposed 
to  go  on  both  in  the  individual,  as  his  thought  develops  and 
his  knowledge  expands,  and  in  the  race,  as  shown  by  its 
history.     By  adopting  this  notion,  we  may  hope  to  show 
also  that  there  is  no  fundamental  difference  in  kind  between 
the   various   intellectual   operations.     Judgment   and   Infer- 
ence, for  example,  will  appear  as  stages  in  the  one  intellec- 
tual process,  and  the  relation  between  Induction  and  Deduc- 
tion, as  each  having  its  own  work  to  do,  will  become  evident. 
§  77.    The  Law  of  Evolution  and  its  Application  to  Logic. 
—  The  most  striking  characteristic  of  any  organism  at  a 
low  stage  of  development   is  its  almost  complete  lack  of 
structure.     An  amoeba,  for  example,  can  scarcely  be  said 


3 1 8    judgment  as  the  Elementary  Process  of  Thought 

to  have  any  structure;  it  is  composed  of  protoplasm  which 
is  almost  homogeneous,  or  of  the  same  character  throughout. 
When  we  compare  an  amoeba,  however,  with  an  animal 
much  higher  in  the  scale  of  life,  e.g.  a  vertebrate,  a  great 
difference  is  at  once  evident.  Instead  of  the  simple,  homo- 
geneous protoplasm,  the  organism  is  composed  of  parts 
which  are  unlike,  or  heterogeneous,  such  as  bones,  muscles, 
tendons,  nerves,  blood-vessels,  etc.  In  Mr.  Spencer's  lan- 
guage, there  has  been  a  change  from  a  state  of  homogeneity,  to 
one  of  heterogeneity.  The  process  of  evolution  from  the  lower 
organism  to  the  higher  has  brought  with  it  a  differentiation 
of  structure.  Thit  is,  in  the  amoeba  there  are  no  special 
organs  of  sight,  or  hearing,  or  digestion,  but  all  of  these  acts 
seem  to  be  performed  by  any  part  of  the  organism  indiffer- 
ently. In  the  vertebrate,  on  the  other  hand,  there  is  division 
of  labour,  and  a  separate  organ  for  each  of  these  functions. 
One  may  also  notice  that  the  same  change  is  observable 
when  the  acts  or  functions  performed  by  a  lower  organism 
are  compared  with  those  of  a  higher.  The  life  of  the  amoeba 
seems  to  be  limited  almost  entirely  to  assimilation  and  repro- 
duction; while,  when  we  advance  from  the  lower  animals 
to  the  higher,  and  from  the  higher  animals  to  man,  there  is 
an  ever-increasing  complexity  and  diversity  in  the  char- 
acter of  the  actions  performed.  We  thus  see  how  the  process 
of  evolution  involves  differentiation  both  of  structure  and 
of  function,  in  passing  from  the  homogeneous  to  the  hetero- 
geneous. 

But  differentiation,  or  increase  in  diversity,  is  only  one 
side  of  the  process  of  evolution.  As  we  pass  from  a  lower  to 
a  higher  stage,  the  various  parts  of  an  organism  are  seen  to 
become  more  essential  to  one  another.     If  certain  plants  or 


§  yj.    Laiv  of  Evolution  and  its  Application  to  Logic     319 

low  animal  organisms  are  divided  into  several  parts,  each 
part  will  go  on  living.  Its  connection  with  the  other  parts 
does  not  seem  to  have  been  at  all  necessary  to  it.  But  when 
we  are  dealing  with  higher  forms  of  life,  each  part  is  seen 
to  have  its  own  particular  function,  and  to  be  essential  to 
the  other  parts,  and  to  the  organism  as  a  whole.  In  other 
words,  the  parts  now  become  members,  and  the  whole  is 
not  simply  an  aggregation  of  parts  or  pieces,  but  is  consti- 
tuted by  the  necessary  relation  of  the  members  to  one 
another.  The  more  highly  evolved  the  whole  with  which 
we  are  dealing,  the  more  closely  connected  and  essential 
to  one  another  are  the  various  parts  seen  to  be.  It  becomes 
increasingly  true  that  if  one  member  suffers,  all  the  other 
members  suffer  along  with  it.  The  same  principle  is  illus- 
trated by  the  relation  of  classes  and  individuals  in  modern 
society.  In  spite  of  the  conflicts  between  capital  and  labour, 
between  rich  and  poor,  it  is  becoming  increasingly  evident 
that  the  unity  of  society  is  more  fundamental  than  its  dif- 
ferences and  antagonisms. 

Evolution,  then,  not  only  exhibits  a  constant  process  of 
differentiation,  and  a  constant  increase  in  the  diversity  of 
parts  and  organs,  but  there  goes  along  with  this  what  might 
be  called  a  process  of  unification,  whereby  the  parts  are 
brought  into  ever  closer  and  more  essential  relation  to  one 
another.  In  this  way,  a  real  or  organic  whole,  as  opposed 
to  a  mere  aggregate,  is  formed.  This  is  what  Mr.  Spencer 
calls  the  process  of  integration;  and  it  accompanies,  as 
we  have  seen,  what  the  same  writer  calls  differentiation. 

The  application  of  this  general  law  of  evolution  to  the 
development  of  the  thinking  process  is  not  difficult.  We 
shall  expect  to  find  that  thinking,  in  its  first  beginnings, 


320    Judgment  as  the  Elementary  Process  of  Thouglit 

both  in  the  individual  and  in  the  race,  will  be  much  less 
complex  and  differentiated  than  at  a  higher  stage.  That 
is,  the  earliest  or  simplest  thinking  tends  to  take  things  in 
a  lump,  without  making  any  distinctions.  The  infant,  for 
example,  does  not  distinguish  one  person  from  another,  or 
perhaps  does  not  distinguish  even  the  parts  of  its  own  body 
from  surrounding  objects.  Now,  it  is  clear  that  intellectual 
development,  growth  in  knowledge,  must  in  the  first  place 
involve  differentiation.  What  is  complex  must  be  analyzed 
or  separated  into  its  various  parts.  Things  which  are  differ- 
ent must  be  distinguished  and  clearly  marked  off  from  one 
another.  The  development  of  thought  implies,  then,  as  one  of 
its  moments,  discrimination  or  analysis  —  what  we  previously 
called  differentiation. 

The  other  moment  of  the  law  of  evolution,  integration, 
also  finds  a  place  in  the  development  of  thought,  and  goes 
hand  in  hand  with  the  former.  The  child  and  the  unedu- 
cated man  not  only  often  fail  to  make  distinctions  where 
these  really  exist,  but  the  parts  of  their  knowledge  are  frag- 
mentary, and  have  little  or  no  relation  to  one  another.  The 
various  pieces  of  their  knowledge  are  like  the  parts  of  the 
amoeba — they  may  be  increased  or  diminished  without 
themselves  undergoing  any  change.  But,  in  order  to  pass 
from  a  lower  to  a  higher  intellectual  point  of  view,  —  to 
become  better  educated,  in  a  word,  —  it  is  necessary  to  see 
the  way  in  which  the  various  pieces  of  our  knowledge  are 
connected  and  dependent  upon  one  another.  It  is  not  enough 
to  analyze  and  keep  separate. things  which  are  distinct,  but 
it  is  also  necessary  to  understand  how  the  various  parts  of 
our  knowledge  are  inter-related  and  essentially  dependent  on 
Dne  another.     In  other  words,  we  may  say  that  it  is  character- 


§  yy.   Law  of  Evolution  and  its  Application  to  Logic     321 

istic  of  our  intelligence  to  endeavour  to  put  things  together  so 
as  to  form  a  whole,  or  system  of  interconnected  parts.  And 
the  more  completely  it  is  able  to  do  this  (provided  that  the 
process  of  differentiation  has  also  made  a  corresponding  ad- 
vance), the  higher  is  the  stage  of  development  which  has  been 
attained.  The  ideal  of  knowledge,  or  of  complete  intellectual 
development,  would  be  to  understand  the  oneness  and  rela- 
tion of  everything  which  exists,  even  of  all  those  things 
which  seem  now  to  be  entirely  different  in  kind.  A  know- 
ledge of  any  one  fact  would  then  carry  with  it  a  knowledge 
of  every  other  fact.  Or,  rather,  our  knowledge  would  be  so 
completely  unified,  that  each  part  would  show  the  nature  of 
the  whole  or  system  to  which  it  belongs;  just  as  a  leaf  of  a 
plant,  or  a  tooth  of  an  animal,  may  be  sufficient  to  tell  the 
naturalist  of  the  wholes  to  which  they  belong. 

This,  of  course,  will  always  remain  an  ideal;  but  it  is 
in  this  direction  that  thinking  actually  develops.  It  is  a 
step  in  advance  to  discover  the  reasons  for  any  fact  which 
one  previously  knew  as  a  mere  fact.  For,  to  discover  the 
reasons  for  a  fact,  is  to  bring  it  into  connection  with  other 
facts,  to  see  them  no  longer  as  isolated  and  independent, 
but  as  belonging  together  to  one  group  or  system  of  facts. 
And  the  further  the  process  of  explanation  goes  on,  the  more 
completely  is  our  knowledge  unified  and  related. 

There  is,  however,  another  fact  implied  in  the  very  nature 
of  evolution  t  of  which  logic,  as  well  as  the  other  sciences, 
may  take  advantage.  We  have  assumed  that  the  more  com- 
plete and  difficult  kinds  of  thinking  have  grown  or  devel- 
oped from  simpler  types  of  the  same  process,  and  not  from 
something  different  in  kind.  It  will  therefore  follow,  that 
the  essential  characteristics  of  the  thinking  process  may  be 


322    Judgment  as  the  Elementary  Process  of  Thought 

discovered  in  its  simplest  and  most  elementary  form.  It 
is  found  that  all  the  essential  functions  of  the  fully  developed 
organism  are  discharged  by  the  primitive  cell.  And  be- 
cause it  is  easier  to  study  what  is  simple  than  what  is  com- 
plex, the  cell  is  taken  as  the  starting-point  in  biology.  Simi- 
larly, there  will  be  an  advantage  in  beginning  with  the  sim- 
plest and  most  elementary  forms  of  thinking.  What  is 
found  true  of  these  simple  types  of  thought,  may  be  assumed 
to  be  essential  to  the  thinking  process  as  such. 

§  78.  Judgment  as  the  Starting-point.  — What,  then, 
is  the  simplest  form  of  thinking  ?  What  shall  we  take  as 
a  starting-point,  which  will  correspond  to  the  cell  in  biology, 
or  the  elementary  process  in  psychology  ?  To  answer  this 
question,  it  is  not  necessary  first  to  decide  where  in  the  scale 
of  animal  life  that  which  we  are  entitled  to  call  thinking 
actually  begins.  We  shall  not  be  obliged  to  discuss  the 
much-debated  question,  whether  or  not  dogs  think.  Wher- 
ever thinking  may  be  found,  it  is  essentially  an  activity  of 
the  mind.  When  it  is  present,  that  is,  there  is  always  intel- 
lectual work  done,  something  interpreted  or  put  together, 
and  a  conclusion  reached.  One  may  perhaps  say  that  think- 
ing is  simply  the  way  in  which  the  mind  puts  two  and  two 
together  and  sees  what  the  result  is.  It  implies  that  the 
mind  has  waked  up  to  the  significance  of  things,  and  has 
interpreted  them  for  itself.  Suppose  that  one  were  sitting  in 
one's  room  very  much  engaged  with  some  study,  or  wrapped 
up  in  an  interesting  book,  and  suppose  that  at  the  same  time 
the  sound  of  a  drum  should  fall  upon  one's  ears.  Now,  the 
sound  sensations  might  be  present  to  consciousness  without 
calling  forth  any  reaction  on  the  part  of  the  mind.  That 
is,  we  might  be  so  intent  on  our  book  that  we  should  not 


§  7$.  Judgment  as  the  Starting-point  323 

wake  up,  as  we  have  been  saying,  to  the  meaning  or  sig- 
nificance of  the  drum-taps;  or  perhaps  not  even  to  the  fact 
that  they  were  drum-taps  at  all.  But  if  the  mind  did  react 
upon  the  sound  sensations,  it  would  try  to  interpret  them, 
or  put  them  together  so  as  to  give  them  a  meaning.  As  a 
result,  some  conclusion  would  be  reached,  as,  for  example, 
'  the  drum  is  beating';  or  sufficient  intellectual  work  may 
have  been  done  to  give  as  a  conclusion,  '  that  is  the  Salva- 
tion Army  marching  up  the  street.'  In  any  case,  it  is  of  the 
greatest  importance  to  notice  that  the  conclusion  does  not 
come  into  our  minds  from  without,  but  that  it  is  the  product 
of  the  mind's  own  activity,  as  has  been  described.  It  is 
not  true,  in  other  words,  that  knowledge  passes  into  our 
minds  through  the  senses;  it  is  only  when  the  mind  wakes 
up  to  the  meaning  of  sensations,  and  is  able  to  put  them  to- 
gether and  interpret  them,  that  it  gains  any  knowledge. 

Now,  the  simplest  form  of  such  an  act  of  thought  is  called 
a  judgment.  Judgment,  we  may  say,  is  a  single  intellec- 
tual act  of  the  kind  we  have  described;  and  its  conclusion 
is  expressed  by  means  of  a  Proposition;  as,  for  example, 
'  the  grass  is  green,'  '  the  band  is  playing.'  In  accordance 
with  general  usage,  however,  we  may  use  the  term  '  Judg- 
ment '  for  both  the  act  itself  and  its  result.  And  the  word 
1  Proposition  '  will  then  denote  the  external  expression  in 
speech  or  writing  of  the  product  of  an  act  of  judgment. 

In  our  investigation  of  the  nature  of  thought,  then,  we 
must  begin  with  Judgment.  There  are  three  things  which 
we  shall  have  to  do:  (1)  To  endeavour  to  discover  the  funda- 
mental characteristics  of  this  simple  type  of  thinking;  (2)  To 
show  the  various  forms  which  it  assumes,  or  to  describe 
the  different  kinds  of  Judgment;  and  (3)  To  trace  the  process 


324    Judgment  as  the  Elementary  Process  of  Thought 

by  which  Judgment  expands  into  the  more  complete  logica\ 
form  of  Inference.  Before  any  of  these  questions  are  con- 
sidered, however,  it  is  necessary  to  meet  a  very  serious  objec- 
tion to  our  whole  procedure  of  beginning  with  Judgment 
as  the  elementary  process  of  thinking. 

§  79.  Concepts  and  Judgment.  —  In  the  last  section, 
we  endeavoured  to  show  that  Judgment  is  the  elementary 
process  of  thought,  and  that  with  it  all  knowledge  begins. 
The  same  position  was  also  maintained  in  an  earlier  chap- 
ter (§  n).  This  view,  however,  may  seem  to  be  contra- 
dicted by  the  treatment  of  Judgment  usually  found  in  logical 
text-books. 

Judgment,  it  is  said,  is  expressed  by  a  proposition;  and  a 
proposition  is  made  up  of  three  parts,  subject,  predicate, 
and  copula.  Thus  in  the  proposition  '  iron  is  a  metal,' 
'  iron '  is  the  subject,  '  a  metal '  the  predicate,  and  the  two 
terms  are  joined  or  united  by  means  of  the  copula  'is.'  A 
Judgment  is  therefore  denned  as  an  act  of  joining  together, 
or,  in  negative  judgments,  of  separating,  two  concepts  or 
ideas.  If  this  account  be  accepted,  it  follows  that  the  ideas 
of  which  the  judgment  is  composed  (iron  and  metal,  in 
the  example  given  above)  are  pieces  of  knowledge  which 
precede  the  judgment  itself.  And  the  act  by  which  these  log- 
ical ideas  (or,  as  they  are  usually  called,  concepts)  are  formed 
must  also  be  earlier  and  more  fundamental  than  the  act  of 
judging.  It  is  therefore  held  that  logic  should  begin  with 
concepts,  which  are  the  elements  out  of  which  judgments 
are  compounded,  and  that  the  first  logical  act  consists  in  the 
conception  or  simple  apprehension  of  the  ideas  or  concepts. 

It  is  necessary  to  examine  this  position  very  carefully. 
What  is  maintained  is  that  a  process  of  forming  concepts, 


§  79-    Concepts  and  Judgment  325 

or  logical  ideas,  presumably  quite  distinct  from  the  activity 
of  judgment,  necessarily  precedes  the  latter.  Before  it  is 
possible  to  judge  that  '  iron  is  a  metal,'  for  instance,  one 
must  have  gained,  by  means  of  Conception  or  Apprehension, 
the  ideas  denoted  by  the  subject  and  predicate  of  this  proposi- 
tion. Judgments,  that  is,  are  made  or  compounded  out  of 
something  different  from  themselves. 

It  may  be  well  to  begin  the  defence  of  our  own  position 
by  noting  what  is  undoubtedly  true  in  what  has  just  been 
stated.  In  making  a  judgment  like  '  iron  is  a  metal,'  it  is, 
of  course,  necessary  to  have  the  concept  'iron,'  and  the 
concept  '  metal.'  But  what  is  implied  in  having  a  concept 
of  anything  ?  Let  us  suppose  that  a  person  is  making  the 
above-mentioned  judgment  for  the  first  time  —  that  is, 
really  drawing  a  conclusion  for  himself,  and  not  merely 
repeating  words.  He  would  begin,  we  may  say,  with  the 
concept  'iron.'  But  if  this  concept  is  more  than  a  mere 
word,  if  it  really  means  anything,  it  must  have  been  formed 
by  a  number  of  judgments.  The  concept  'iron,'  if  it  has 
any  significance  for  the  person  using  it,  means  a  definite 
way  of  judging  about  some  substance — that  it  is  hard, 
malleable,  tough,  etc.  The  greater  the  number  of  judg- 
ments which  the  concept  represents,  the  more  meaning  or 
significance  it  has ;  apart  from  the  judgment,  it  is  a  mere 
word,  and  not  a  thought  at  all. 

To  admit,  then,  that  in  judging  we  always  start  from 
some  concept,  does  not  imply  that  there  is  a  different  form  of 
intellectual  activity  prior  to  judgment,  which  furnishes  the 
latter  with  ready-made  material  for  its  use.  But,  as  we 
have  seen,  in  ordinary  judgments  like  the  example  with 
which  we  have  been  dealing,  the  new  judgment  is  a  further 


326    Judgment  as  the  Elementary  Process  of  Thought 

expansion  or  development  of  a  previous  set  of  judgments 
which  are  represented  by  the  concept.  The  concept,  then, 
stands  for  the  series  of  judgments  which  have  already  been 
made.  Language  comes  to  the  aid  of  thought,  and  makes  it 
possible  to  gather  up  such  a  set  of  judgments  and  represent 
them  by  a  single  expression  —  often  by  a  single  word.  Every 
word  which  is  the  name  of  some  logical  concept  represents 
intellectual  work  — the  activity  of  judgment  — in  its  forma- 
tion. In  learning  our  own  language,  we  inherit  the  word 
without  doing  the  work.  But  it  must  never  be  forgotten 
that  the  word  in  itself  is  not  the  concept.  To  make  the 
thought  our  own,  to  gain  the  real  concept,  it  is  necessary  to 
draw  out  or  realize  to  ourselves  the  actual  set  of  judgments 
for  which  the  word  is  but  the  shorthand  expression. 

The  view  which  regards  the  judgment  as  a  compound  of 
two  parts  —  subject  and  predicate  —  rests  upon  the  substitu 
tion  of  words  for  thoughts.  It  analyzes  the  proposition  (the 
verbal  or  written  expression  of  the  judgment),  instead  of  the 
judgment  itself.  In  the  proposition,  the  parts  do  exist 
independently  of  each  other.  The  subject  usually  stands 
first,  and  is  followed  by  the  predicate.  But  there  is  no  such 
order  of  parts  in  a  judgment.  When  one  judges, '  it  is  raining,' 
or,  'that  is  a  drum,'  the  piece  of  knowledge  is  one  and  indi- 
visible. And  the  act  by  which  this  knowledge  is  gained  is 
not  an  external  process  of  joining  one  part  to  another,  but 
is  an  intellectual  reaction  by  which  we  recognize  that  some- 
thing, not  previously  understood,  has  a  certain  meaning  or 
significance. 

Again,  it  is  only  when  concepts  are  identified  with  the  words 
which  make  up  the  parts  of  the  proposition,  that  they  can  be 
regarded  as  ready-made  existences  which  are  quite  independ- 


§  79-    Concepts  and  Judgment  327 

ent  of  their  connection  in  a  judgment.  The  terms  '  iron '  and 
'metal '  are  separable  parts  of  the  proposition  and  exist  inde- 
pendently of  their  connection  with  it.  The  conclusion  has 
been  therefore  drawn  that  concepts  had  a  like  independence 
of  judgments,  but  might  enter  into  the  latter  and  form  a  part 
of  them  without  affecting  their  own  nature  in  any  way. 
But,  as  we  have  already  seen,  the  concept  has  no  meaning 
apart  from  the  series  of  judgments  which  it  represents.  And, 
as  thinking  goes  on,  and  new  judgments  are  made,  its  nature 
is  constantly  changing.  In  short,  concepts  are  not  dead 
things,  but  living  thoughts  which  are  in  constant  process  of 
development. 

The  objection,  then,  which  urges  that  conception  is  a  logical 
process  that  is  prior  to  judgment,  turns  out,  when  rightly 
understood,  to  be  no  objection  at  all.  For,  in  the  light  of  what 
has  been  already  said,  it  only  amounts  to  this:  In  making  new 
judgments  regarding  anything,  we  must  set  out  from  what 
we  already  know  of  it,  as  represented  by  the  judgments  already 
made.  That  is,  the  starting-point  for  a  new  judgment  is  the 
concept  or  series  of  judgments  which  represents  the  present 
state  of  our  knowledge.  The  progress  of  knowledge  is  not 
from  the  unknown  to  the  known,  but  from  a  state  of  partial 
and  incomplete  knowledge  to  one  of  greater  perfection.  Thus 
the  judgment '  gold  is  malleable'  (supposing  it  to  be  a  genuine 
judgment  made  for  the  first  time)  adds  to,  or  develops 
farther,  our  existing  knowledge  of  gold,  as  represented  by  a 
series  of  judgments  previously  made  regarding  it. 

It  may  be  urged,  however,  that  not  every  judgment  can  grow  out 
of  previous  judgments  in  this  way.  For,  if  we  go  back  far  enough, 
we  must  reach  some  judgment  which  is  absolutely  first,  and  which 
presupposes  no  antecedent  judgment.     This  is  like  the  paradox 


328     Judgment  as  the  Elementary  Process  of  Thought 

regarding  the  origin  of  life.  If  all  judgments  are  derived  from  an< 
tecedent  judgments,  how  was  it  possible  for  the  first  one  to  arise? 
It  will,  perhaps,  be  sufficient  answer  to  deny  the  existence  of  the 
paradox.  Consciousness  must  be  regarded  as  having  from  the  first 
the  form  of  a  judgment.  No  matter  how  far  one  goes  back  in  the 
history  of  consciousness,  one  will  always  find,  so  long  as  conscious- 
ness is  present  at  all,  some  reaction,  however  feeble,  upon  the 
content,  and  something  like  knowledge  resulting.  Even  the  con- 
sciousness of  the  newly  born  infant  reacts,  or  vaguely  judges, 
in  this  way.  These  primitive  judgments  are,  of  course,  very  weak 
and  confused,  but  they  serve  as  starting-points  in  the  process  of  in- 
tellectual development.  Growth  in  knowledge  is  simply  the  pro- 
cess by  means  of  which  these  vague  and  inarticulate  judgments  are 
developed  and  transformed  into  a  completer  and  more  coherent 
experience. 

REFERENCES 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  pp.  9-16. 
F.  H.  Bradley,  The  Principles  of  Logic,  Bk.  I.,  Ch.  I. 

B.  Bosanquet,  Logic,  Vol.  I.,  Ch.  I.,  §§  1-6. 

H.  Lotze,  Logic  (Eng.  trans.),  Vol.  I.,  pp.  13-61. 

C.  Sigwart,  Logic,  §§40-42. 

L.  T.  Hobhouse,  The  Theory  of  Knowledge,  Pt.  I.,  Chs.  I.  and  II. 


CHAPTER   XXII 

THE   MAIN   CHARACTERISTICS   OF  JUDGMENT 

§  80.  The  Universality  of  Judgments.  —  We  have  now 
to  examine  the  nature  of  Judgment  a  little  more  closely  than 
has  been  done  hitherto.  In  the  first  place,  we  note  that 
all  judgments  claim  universality.  There  are,  however, 
several  kinds  of  universality,  and  more  than  one  sense  in 
which  a  judgment  may  be  said  to  be  universal.  We  speak  of 
a  universal  judgment  (more  properly  of  a  universal  propo- 
sition), when  the  subject  is  a  general  term,  or  is  qualified  by 
some  such  word  as  'all,'  or  '  the  whole.'  And  we  distinguish 
from  it  the  particular  judgment,  where  the  subject  is  only  the 
part  of  some  whole,  and  is  usually  preceded  by  '  some,'  or 
by  other  partitive  words.  But  here  we  have  no  such  dis- 
tinction in  mind;  we  are  speaking  of  the  universality  which 
belongs  to  the  very  nature  of  Judgment  as  such,  and  which 
is  shared  in  by  judgments  of  every  kind. 

When  we  say  that  judgments  are  universal,  in  the  sense 
in  which  the  word  is  now  used,  we  mean  that  the  conclusions 
which  they  reach  claim  to  be  true  for  every  one.  No  matter 
what  the  subject  and  the  predicate  may  be,  a  judgment,  e.g. 
'  man  is  mortal,'  comes  forward  as  a  fact  for  all  minds.  We 
have  shown  in  the  last  chapter  that  it  is  by  judging,  or  putting 
things  together  for  itself,  that  the  human  mind  gains  know- 
ledge. Now,  the  assumption  upon  which  this  process  is 
based  is  that  the  result  thus  reached  —  knowledge  —  is  not 

329 


330  Tfte  Main  Characteristics  of  Judgment 

something  merely  individual  and  momentary  in  character. 
When  I  judge  that  '  two  and  two  are  four,'  or  that  '  iron  has 
magnetic  properties,'  the  judgment  is  not  merely  a  statement 
of  what  is  going  on  in  my  individual  consciousness ;  but  it 
claims  to  express  something  which  is  true  for  other  persons 
as  well  as  for  me.  It  professes  to  deal  with  facts  which  are 
true,  and  in  a  sense  independent  of  any  individual  mind. 
The  judgments  by  which  such  conclusions  are  reached  are 
universal,  then,  in  the  sense  that  they  are  asserted  as  true  for 
every  one  and  at  all  times.  The  word  '  objective  '  has  essen- 
tially the  same  meaning.  Although  each  man  reaches  truth 
only  by  actually  judging  for  himself,  yet  truth  is  objective, 
out  there  beyond  his  individual  or  '  subjective '  thought, 
shared  in  by  all  rational  beings.  The  assumption  upon 
which  all  argument  proceeds  is  that  there  is  an  objective  stand- 
ard, and  that  if  people  can  be  made  to  think  they  will  arrive 
at  it.  Thought  is  in  essence  a  process  of  self-criticism;  for 
it  has  in  itself  its  own  standard  of  truth,  which  comes  to  light 
in  and  through  the  process  of  development. 

(i)  The  only  alternative  to  this  position  is  scepticism,  or  pure 
individualism.  If  Judgment  is  not  universal  in  the  sense  that  it 
reaches  propositions  which  are  true  for  everybody,  it  is  of  course  im- 
possible to  find  any  standard  of  truth  at  all.  The  judgments  of  any 
individual  in  that  case  would  simply  have  reference  to  what  seemed 
true  to  him  at  the  moment,  but  could  not  be  taken  to  represent  any 
fixed,  or  permanent,  truth.  Indeed,  if  one  regards  Judgment  as 
dealing  merely  with  particular  processes  in  an  individual  mind,  the 
ordinary  meanings  of  truth  and  falsehood  are  completely  lost,  and  it 
becomes  necessary  to  give  a  new  definition  of  the  words.  This  was 
the  position  of  the  Sophists  at  the  time  of  Socrates  (cf.  §  5).  Each 
individual  man  was  declared  to  be  the  measure  of  what  is  true  and 


§  8 1.    The  Necessity  of  Judgments  331 

false,  as  well  as  of  what  is  good  and  bad.  There  is  thus  no  other 
standard  of  truth  or  value  than  the  momentary  judgment  (or  ca- 
price) of  the  individual.  This  is,  in  a  way,  the  rednctio  ad 
absurdum  of  scepticism. 

The  common  nature  of  truth,  as  something  in  which  all  can 
share,  presupposes,  then,  a  common  mode  of  thinking  or  judging  on 
the  part  of  all  rational  beings.  And  it  is  this  universal  type  or  form 
of  knowing  with  which  logic  deals.  The  question  as  to  whose 
thought  is  investigated,  or  in  what  individual  mind  the  thought 
takes  place,  is  in  itself  of  no  importance.  The  consciousness  of  a 
savage  differs  very  greatly  from  that  of  an  educated  man ;  it  is  much 
less  complex  and  less  highly  developed.  But  yet,  in  spite  of  the 
enormous  differences,  there  exists  in  both  an  intelligence,  or  way  of 
thinking,  which  shows  the  same  essential  character,  and  operates 
according  to  the  same  fundamental  laws. 

§  81.  The  Necessity  of  Judgments.  — The  second  char- 
acteristic which  we  note  as  belonging  to  Judgment  is  necessity. 
By  this  we  mean  that  when  a  person  judges,  he  is  not  free 
to  reach  this  or  that  conclusion  at  will.  As  an  intellectual 
being,  he  feels  bound  to  judge  in  a  certain  way.  This  is 
sometimes  expressed  by  saying  that  we  cannot  believe  what 
we  choose  ;  we  must  believe  what  we  can. 

In  many  of  the  ordinary  judgments  of  everyday  life,  which 
are  made  without  any  clear  consciousness  of  their  grounds, 
logical  necessity  is  implicitly  present  as  an  immediate  feeling 
of  certainty.  In  cases  of  this  kind,  we  simply  identify  our- 
selves with  the  judgment,  and  feel  that  it  is  impossible  that 
it  can  be  false.  But,  of  course,  no  judgment  can  claim  to  be 
necessary  in  its  own  right.  Its  necessity  comes  from  its  con- 
nection with  other  facts  which  are  known  to  be  true.  Or,  in 
logical  terms,  we  may  say  that  it  comes  from  reasons  or  prem- 


332  The  Main  Characteristics  of  Judgment 

ises  which  support  it.  And  one  should  always  be  ready  to 
show  the  grounds  or  reasons  upon  which  one's  feeling  of  ne- 
cessity rests.  But  in  ordinary  life,  as  we  have  said,  it  is  not 
unusual  to  regard  a  conclusion  as  necessary,  without  clearly 
realizing  the  nature  of  the  reasons  by  which  it  is  supported. 
An  uneducated  man  is  rarely  able  to  go  back  and  discover  the 
reasons  for  his  belief  in  any  statement  of  which  he  is  con- 
vinced. If  you  question  his  assertion,  he  feels  that  you  are 
reflecting  upon  his  veracity,  and  consequently  grows  angry. 
In  the  feeling  of  immediate  necessity  or  conviction,  he  iden- 
tifies himself  with  the  judgment,  and  does  not  see  that  the 
criticism  is  not  directed  against  the  latter,  but  against  the 
grounds  by  which  it  is  supported. 

In  this  distinction  between  necessity  that  is  merely  felt, 
and  the  necessity  that  is  conscious  of  its  own  grounds,  we  see 
the  direction  in  which  judgment  must  develop.  In  the  evolu- 
tion of  thought,  we  gradually  become  conscious  of  the 
grounds  upon  which  our  judgments  are  made.  That  is,  the 
simple  judgment,  which  seems  to  stand  in  isolation,  is  seen 
to  expand  so  as  to  include  its  reasons  as  an  organic  part  of 
itself.  By  itself,  it  is  only  a  fragment  of  a  more  complete 
and  widely  embracing  thought.  The  feeling  of  necessity  is  an 
evidence  of  its  dependence  and  connection,  though  this  de- 
pendence and  connection  upon  other  facts  may  not  be  clearly 
understood.  But  what  is  implicit  must  be  made  explicit; 
the  necessity  which  is  merely  felt  to  belong  to  the  simple 
judgment  must  be  justified,  by  showing  the  grounds  or  rea- 
sons upon  which  it  rests.  And,  for  this  purpose,  the  simple 
judgment  has  to  be  brought  into  relation  with  other  facts 
and  judgments  which  are  outside  of  it,  yet  constitute  its 
reasons,  or  are  necessary  to  support  it.      In  other  words,  it 


§  8 1.    The  Necessity  of  Judgments  333 

must  develop  into  an  inference.  As  a  matter  of  fact,  the 
same  form  of  words  as  used  by  different  persons,  or  by  the 
same  person  at  different  times,  may  express  either  a  judg- 
ment or  an  inference.  Thus,  '  the  price  of  wheat  rose  after 
the  war  began '  might  express  either  a  simple  historical  fact, 
which  is  accepted  from  experience  or  from  hearsay,  or  it 
might,  in  the  mouth  of  a  person  acquainted  with  the  laws  cf 
supply  and  demand,  be  the  necessary  conclusion  of  a  number 
of  premises.  Again,  a  child  might  read  that,  '  the  travelers 
found  great  difficulty  in  breathing  when  they  reached  the  top 
of  the  mountain,'  accepting  this  as  a  simple  statement  of  fact. 
If  he  were  to  read  this  same  statement  some  years  later,  how- 
ever, he  would  probably  connect  it  at  once  with  other  facts 
regarding  the  nature  of  the  atmosphere,  and  the  action  of 
gravity,  and  so  perceive  at  once  its  inferential  necessity. 

(1)  According  to  the  view  which  has  just  been  stated,  necessity  is 
not  a  property  which  belongs  to  any  judgment  in  itself,  but  some- 
thing which  arises  through  its  dependence  upon  other  judgments. 
In  other  words,  necessity  is  always  mediate,  not  immediate.  This 
view,  however,  differs  from  a  theory  that  was  once  generally  re- 
ceived, and  has  some  adherents,  even  at  the  present  time,  especially 
among  thinkers  who  belong  to  the  Scottish  or  'common-sense' 
school.  In  dealing  with  the  facts  of  experience,  we  always  explain 
one  fact  by  referring  it  to  a  second,  and  that  second  by  showing  its 
dependence  upon  some  third  fact,  and  so  on.  Thus  the  movement 
of  the  piston-rod  in  an  engine  is  explained  by  the  pressure  of 
steam,  and  this  is  due  to  the  expansive  power  of  heat,  and  heat 
is  caused  by  combustion  of  fuel,  etc.  We  are  thus  referred  back  in 
our  explanations  from  one  fact  or  principle  to  another,  without 
ever  reaching  anything  that  does  not  require  in  its  turn  to  be 
explained. 


334  The  Main  Characteristics  of  Judgment 

Now,  it  is  said  that  this  process  cannot  go  on  forever;  for  if  it 
did  there  could  be  no  final  or  complete  knowledge;  the  whole 
system  would  be  left  hanging  in  the  air.  There  must,  therefore, 
it  is  argued,  be  some  ultimate  facts  which  furnish  the  support  for 
the  world  of  our  experience,  some  principle  or  principles  which  are 
themselves  necessary  and  do  not  require  any  proof.  That  is,  there 
must  be  certain  propositions  which  are  immediately  necessary,  and 
which  serve  as  the  final  explanation  for  everything  else.  Now,  it  is 
clear  that  such  propositions  must  be  entirely  different  in  character 
from  the  ordinary  facts  of  experience,  since  their  necessity  belongs 
to  their  own  nature,  and  is  not  derived  from  any  other  source.  It 
had  to  be  supposed,  therefore,  that  they  stood  upon  a  different 
plane,  and  were  not  derived  from  experience.  To  explain  the  su- 
perior kind  of  certainty  which  they  were  assumed  to  possess,  it  was 
supposed  that  they  were  present  in  the  mind  at  birth,  or  were  innate. 
They  have  also  been  called  necessary  truths,  a  priori  truths,  and 
fundamental  first  principles,  in  order  to  emphasize  their  supposed 
distinction  from  facts  which  are  derived  from  experience. 

When  one  regards  knowledge  as  an  internal  process  of  growth 
or  development,  however,  where  each  element  plays  its  part,  as  do 
the  members  of  a  living  body,  the  inadequacy  of  any  view  which 
looks  for  a  mechanical  basis  for  knowledge  is  apparent.  What 
is  present  in  experience  is  a  moving  system  of  functions,  not  a 
structure  of  fixed  mechanical  parts,  such  as  exist,  for  example, 
in  a  building. 

§  82.    Judgment  involves  both  Analysis  and  Synthesis.  — 

The  business  of  our  thought  is  to  understand  the  ways  in 
which  the  various  parts  of  the  real  world  are  related.  And 
a  judgment,  as  we  have  already  seen,  is  just  a  single  act  of 
thought,  — one  step  in  the  process  of  understanding  the 
world.  Now  we  ask:  How  does  Judgment  accomplish  its 
task  ?    Does  it  proceed  altogether  by  analysis,  by  pointing 


§  82.  Judgment  involves  both  Analysis  and  Synthesis     335 

out  the  parts  of  which  things  are  composed,  or  does  it  also 
employ  synthesis  in  order  to  show  how  various  parts  combine 
in  such  a  way  as  to  form  a  whole  ?  Or  is  it  possible  for  both 
these  processes  to  be  united  in  one  and  the  same  act  of  judg- 
ment ? 

Suppose  that  one  actually  makes  the  judgment  for  oneself 
(and  does  not  merely  repeat  the  words  of  the  proposition), 
1  the  rose  has  pinnate  leaves.'  What  has  taken  place  ?  We 
notice,  firstly,  that  a  new  property  of  the  rose  has  been 
brought  to  light;  a  distinction,  or  mark,  has  been  discovered 
in  the  content  '  rose,'  which  was  not  seen  to  belong  to  it  be- 
fore the  judgment  was  made.  So  far,  then,  the  process  is  one 
of  analysis,  of  discovering  the  parts  or  distinctions  of  some- 
thing which  is  at  first  taken,  as  it  were,  in  a  lump.  And  this 
is  a  most  essential  element  in  all  thinking.  In  order  to  know, 
it  is  absolutely  necessary  that  the  differences  between  the 
parts  of  things  should  be  clearly  apprehended,  that  we 
should  not  confuse  things  which  are  unlike,  or  fail  to  make 
proper  distinctions.  If  we  examine  a  number  of  instances 
where  a  real  judgment  is  made,  we  shall  find  that  this  moment 
of  analysis,  or  discrimination,  is  always  present.  Sometimes, 
indeed,  analysis  may  not  seem  to  be  the  main  purpose  of  the 
judgment;  but  if  one  looks  closely,  one  will  always  find  in  a 
judgment  that  elements  which  are  unlike  are  held  apart 
or  discriminated. 

But  let  us  look  again  at  the  same  judgment,  '  the  rose  has 
pinnate  leaves.'  It  is  not  difficult  to  see  that  the  discovery 
of  something  new  in  itself  is  only  one  part  of  what  the  judg- 
ment has  accomplished.  The  judgment  also  affirms  the  union 
of  this  new  discovery  with  the  properties  of  what  we  call 
the  rose.     It  is,  therefore,  from  this  point  of  view,  an  act  of 


336  The  Main  Characteristics  of  Judgment 

synthesis.  It  asserts  that  the  prickly  branches,  fragrant 
flowers,  feather-like  leaves,  and  other  distinctions  are  united 
in  the  one  content  which  we  call  the  rose.  It  does  not  stop 
with  the  mere  assertion,  '  there  is  a  mark  or  distinction,'  but 
it  affirms  that  it  is  a  mark  of  something,  i.e.  that  it  is  united 
with  other  marks  or  properties  to  form  a  concrete  whole.  In 
other  words,  we  may  say  that  every  judgment  affirms  the 
unity  of  the  different  parts,  or  aspects,  of  a  thing;  and  this  is, 
of  course,  synthesis.  From  this  point  of  view,  then,  Judgment 
can  be  defined  as  a  process  of  synthesis,  just  as  we  defined  it 
above  as  one  of  analysis. 

But  how,  it  may  be  asked,  is  it  possible  for  a  judgment  to 
be  both  analytic  and  synthetic  ?  Are  not  these  processes 
directly  opposed  to  each  other  ?  It  is  true  that  there  can  be 
no  doubt  that  this  is  the  case  when  we  are  dealing  with  ma- 
terial things:  pulling  things  to  pieces  is  the  opposite  of  put- 
ting them  together.  When  we  are  doing  the  one  we  cannot 
also  be  doing  the  other.  But  there  is  no  such  opposition 
between  these  processes  when  they  go  on  in  our  minds.  An 
illustration  may  make  this  clear.  Suppose  that  one  is  trying 
to  understand  some  piece  of  mechanism,  say  a  watch;  in 
order  to  be  able  to  see  how  it  goes,  or  judge  correctly  regard- 
ing it,  two  things  are  necessary.  First,  one  must  notice  all 
the  parts  of  which  it  is  composed  —  the  wheels  of  various 
sizes,  springs,  pins,  etc.  But,  in  the  second  place,  one  would 
not  understand  the  watch  until  one  saw  how  all  the  parts 
were  united,  how  one  part  fits  into  another,  and  all  combine 
together  into  one  whole.  We  do  not  mean  that  these  are  two 
steps  which  take  place  in  succession;  as  a  matter  of  fact,  the 
detection  of  the  various  parts,  and  the  perception  of  their 
connection,  go  hand  in  hand.     In  the  process  of  understand- 


§  82.  Judgment  involves  both  Analysis  and  Synthesis     337 

ing  the  watch,  we  have  both  taken  it  to  pieces  and  put  it 
together  again  at  one  and  the  same  time.  Not  really,  of 
:ourse,  but  in  our  thought.  In  the  world  of  material  things, 
as  we  have  said,  only  one  of  these  processes  could  go  on  at  a 
time;  but  in  every  act  of  thinking,  in  every  judgment,  analysis 
and  synthesis  go  hand  in  hand,  and  one  has  no  meaning 
except  with  reference  to  the  other. 

But  the  two  moments  or  factors  of  analysis  and  synthesis, 
although  present  in  every  judgment,  are  not  always  equally 
prominent.  The  main  purpose  of  the  judgment  usually  falls 
on  one  side  or  the  other.  In  a  judgment  like,  '  water  can 
be  divided  into  hydrogen  and  oxygen,'  the  main  emphasis 
seems  to  be  on  the  parts,  and  the  assertion  that  these  ele- 
ments are  parts  of  a  whole,  though  present,  is  only  implied. 
But  when  one  asserts,  '  these  springs  and  wheels  together 
make  up  a  watch,'  it  is  the  nature  of  the  whole  upon  which 
the  emphasis  is  laid,  and  the  separation  or  discrimination  of 
the  parts  is,  as  it  were,  secondary.  It  is  not  difficult  to  see, 
however,  that  the  two  moments  of  Judgment  are  present  in 
both  of  these  cases.  The  difference  consists  in  the  fact 
that  at  one  time  analysis,  and  at  the  other  synthesis,  is  made 
the  main  purpose. 

It  was  at  one  time  supposed  that  analytic  and  synthetic 
judgments  were  entirely  different  in  kind  from  each  other. 
An  analytic  judgment,  it  was  said,  is  one  in  which  the  predi- 
cate is  obtained  by  analyzing,  or  bringing  to  light,  what  is 
contained  in  the  subject.  Thus  the  judgment,  '  all  material 
bodies  fill  space,'  is  analytic;  for  the  predicate  (space-filling) 
is  contained  in  the  very  notion,  or  idea,  of  a  material  body. 
All  that  is  necessary  in  order  to  obtain  the  judgment  is  to 
comprehend  the  meaning  of  the  subject.     An  analytic  judg- 


338  The  Main  Characteristics  of  Judgment 

ment,  then,  adds  nothing  to  our  knowledge.  It  merely 
enables  us  to  bring  to  light  and  express  what  is  contained  in 
the  ideas  we  already  possess.  A  synthetic  proposition,  on 
the  contrary,  was  defined  as  one  in  which  the  predicate  was 
not  already  contained  in  the  subject,  but  which  added  a  new 
element  or  idea  to  it.  'This  body  weighs  ten  pounds,'  fof 
example,  is  a  synthetic  proposition,  for  one  cannot  obtain 
the  predicate  by  analyzing  the  subject.  The  predicate  adds 
a  new  fact  which  must  have  been  derived  from  experience. 

(i)  This  view  is,  of  course,  fundamentally  different  from  the  ac- 
count of  Judgment  which  we  have  just  given.  The  absolute  distinc- 
tion between  analytic  and  synthetic  judgments,  like  the  theory 
that  thought  begins  with  concepts,  arises,  I  think,  from  a  substitu- 
tion of  the  spoken  or  written  proposition  for  the  judgment  itself. 
In  the  proposition  the  subject  seems  to  be  the  starting-point.  We 
have  a  word  or  term  which  appears  to  be  independent  and  capa- 
ble of  standing  alone.  The  question  is,  then,  where  shall  we  find 
the  predicate?  For  example,  in  the  proposition,  'iron  is  an  ele- 
ment,' the  subject  stands  first,  and  the  predicate  comes  later.  It 
seems  possible  then  to  say  that  we  have  first  the  subject  'iron,'  and 
then  join  on  to  it  the  predicate  'element,'  which  has  been  obtained 
either  by  analyzing  the  subject,  or  from  some  previous  experience. 
But  the  proposition,  as  a  collection  of  words,  must  not  be  substituted 
for  the  act  of  judgment.  Judgment,  as  we  have  already  seen,  is  a 
single  act  of  intelligence,  which  at  once  discriminates  and  brings 
into  relation  different  aspects  of  the  whole  with  which  it  is  dealing. 
A  mere  subject  by  itself  has  not  any  intelligible  meaning.  If  one 
hears  the  word  'iron,'  for  example,  the  word  may  call  up  certain 
mental  images ;  but  by  itself  it  is  not  a  complete  thought  or  fact  in 
which  we  can  rest.  '  Well,  what  of  it  ? '  we  say.  The  mind  at  once 
goes  on  to  form  some  judgment  like,  'this  is  iron,'  or  'iron  is  heavy.' 
We  cannot  think  a  term  without  thinking  something  o/it.     In  short, 


§  83.  Constructing  a  System  of  Knowledge         339 

although  the  words  which  form  the  subject  of  a  proposition  are 
relatively  independent,  and  can  be  used  without  the  words  which 
make  up  the  predicate,  in  a  judgment,  on  the  other  hand,  a  subject 
is  only  a  subject  through  its  relation  to  a  predicate.  The  propo- 
sition may  be  divided  into  parts,  but  the  judgment  is  a  single 
thought-activity,  and  cannot  be  divided  (cf.  §  79  ). 

§  83.  Judgment  as  Constructing  a  System  of  Know- 
ledge. —  In  this  section  we  have  not  to  take  account  of  any 
new  characteristic  of  Judgment,  but  rather  to  emphasize  the 
part  it  plays  in  building  up  knowledge.  As  we  have  seen, 
Judgment  works  both  analytically  and  synthetically:  it  dis- 
covers new  parts  and  distinctions,  and  at  the  same  time 
brings  the  parts  into  relation  and  thus  builds  up  a  whole. 
That  is  the  law  according  to  which  thinking  develops,  and  is 
just  what  we  called  differentiation  and  integration  in  a  pre- 
vious section  (§  77). 

It  is  necessary  here,  however,  to  dwell  upon  the  fact  that 
each  judgment  may  be  regarded  as  a  step  in  the  process  of 
building  up  a  system  of  knowledge.  The  emphatic  word 
here  is  '  system,'  and  we  must  be  perfectly  clear  about  its 
meaning.  A  system  is  a  whole  which  is  composed  of  va- 
rious parts.  But  it  is  not  the  same  thing  as  an  aggregate 
or  heap.  In  an  aggregate  or  heap,  no  essential  relation 
exists  between  the  units  of  which  it  is  composed.  In  a  heap 
of  grain,  or  pile  of  stones,  one  may  take  away  any  part  with- 
out the  other  parts  being  at  all  affected  thereby.  But  in  a 
system,  each  part  has  a  fixed  and  necessary  relation  to  the 
whole  and  to  all  the  other  parts.  For  this  reason  we  may  say 
that  a  building,  or  a  piece  of  mechanism,  is  a  system.  Each 
stone  in  the  building,  each  wheel  in  the  watch,  plays  a  part, 
and  is  essential  to  the  whole.     In  things  which  are  the  result 


340  The  Main  Characteristics  of  Judgment 

of  growth,  the  essential  relations  in  which  the  parts  stand  is 
even  more  clearly  evident.  The  various  parts  of  a  plant  or 
an  animal  have  their  own  functions,  but  at  the  same  time 
they  are  so  necessary  to  one  another  that  an  injury  to  one  is 
an  injury  to  all.  We  express  this  relation  in  the  case  of  living 
things  by  saying  that  the  parts  are  organic  to  one  another. 
And,  in  the  same  way,  it  is  not  unusual  to  speak  of  society  as 
an  organism,  in  order  to  express  the  fact  that  the  various 
individuals  of  which  it  is  composed  are  not  independent 
units,  but  stand  in  necessary  relations  to  one  another,  and 
are  all  mutually  helpful  or  hurtful. 

We  have  said  that  Judgment  constructs  a  system  of  know- 
ledge. This  implies,  then,  that  it  is  not  merely  a  process 
of  adding  one  fact  to  another,  as  we  might  add  one  stone  to 
another  to  form  a  heap.  Judgment  combines  the  new  facts 
with  which  it  deals,  with  what  is  already  known,  in  such  a 
way  as  to  give  to  each  its  own  proper  place  in  relation  to  and 
interdependence  with  the  others.  Different  facts  are  not 
only  brought  together,  but  they  are  arranged,  related,  sys- 
tematized. No  fact  is  allowed  to  stand  by  itself,  but  has  to 
take  its  place  as  a  member  of  a  larger  system  of  facts,  and 
receive  its  value  and  meaning  from  this  connection.  Of 
course,  a  single  judgment  is  not  sufficient  to  bring  a  large 
number  of  facts  into  relation  in  this  way.  But  each  judg- 
ment contributes  something  to  this  end,  and  brings  some 
new  fact  into  relation  to  what  is  already  known.  Even  in 
a  simple  judgment  like,  '  that  was  the  twelve  o'clock  whistle,' 
the  constructive  or  systematizing  work  accomplished  is 
evident.  The  auditory  sensation,  which  in  itself,  as  a  mere 
sound,  was  not  a  piece  of  knowledge  at  all,  is  interpreted  in 
such  a  way  as  to  find  a  place  in  the  system  of  experience. 


§  83.   Constructing  a  System  of  Knowledge         341 

One  may  appreciate  what  part  the  judgment  really  plays  by 
remembering  how  the  sound  appeared  before  one  was  able 
to  judge.  There  may  have  been  at  first  a  moment  of  be- 
wilderment — '  What  does  this  mean  ?  '  one  asks.  In  the 
next  moment  the  judgment  is  made:  '  It  is  the  twelve  o'clock 
whistle.'  That  is,  our  thinking  has  constructed  a  meaning 
for  it,  and  brought  it  into  relation  with  the  rest  of  our  know- 
ledge. 

(1)  Every  new  experience  is  thus  brought  into  relation  with  the 
facis  which  we  already  know,  and  is  tested  by  them.  It  has  to  find 
its  place  in  the  system  of  knowledge—  to  join  itself  to  what  is  already 
known.  If  this  is  impossible,  if  what  claims  to  be  a  fact  is  entirely 
opposed  to  what  we  already  know  on  the  same  subject,  it  is  usually 
declared  to  be  false.  Thus,  we  would  refuse  to  believe  that  some 
person  whom  we  know  well  and  respect  was  guilty  of  theft;  for  it 
would  be  impossible  to  connect  such  conduct  with  what  we  already 
know  of  his  character.  And,  similarly,  we  find  it  impossible  to 
believe,  even  although  we  have  the  evidence  of  our  senses,  that  the 
conjurer  has  actually  performed  what  he  professes;  for  to  do  so 
would  often  be  to  reverse  entirely  our  conception  of  natural  laws. 
It  must  not  be  forgotten,  however,  that  the  existing  system  of  know- 
ledge, which  seems  to  serve  as  the  standard  and  test  of  new  facts,  is 
itself  undergoing  constant  modification  through  the  influence  of 
these  facts.  As  new  experiences  are  brought  into  connection  with 
the  existing  body  of  our  knowledge,  there  is  a  constant  rearrange- 
ment and  readjustment  of  the  latter  going  on.  Usually  this  adjust- 
ment is  slight,  and  takes  place  almost  imperceptibly.  But,  in  some 
cases,  a  single  fact  may  be  so  significant  as  completely  to  transform 
what  seemed  to  be  the  accumulated  knowledge  of  years.  The 
experiment  which  Galileo  made  by  dropping  balls  of  different 
weight  from  the  tower  of  Pisa,  made  it  impossible  to  hold  any  longer 
the  old  theory  —  which  seemed  as  certain  as  anything  well  could  be 


34-2  The  Main  Characteristics  of  Judgment 

—  that  the  velocity  with  which  bodies  fall  is  proportional  to  theii 
weight.  Again,  if  theft  were  actually  proved  against  the  man  we 
respect,  that  single  fact  might  be  sufficient  to  force  us  to  give  up 
everything  which  we  supposed  that  we  knew  about  his  character. 
(2)  We  have  said  that  judgment  is  the  process  by  which  know- 
ledge grows  into  a  system.  It  is  by  judging  or  thinking  that  we 
attempt  to  bring  the  various  parts  of  our  experience  into  relation 
with  one  another.  The  degree  to  which  this  has  been  done  is  the 
measure  of  our  intellectual  development.  The  knowledge  of  the 
uneducated  and  unthinking  man,  like  that  of  the  child,  is  largely 
composed  of  unrelated  fragments.  It  is  an  aggregation,  not  a 
system  of  facts.  The  facts  which  go  to  make  it  up  may  quite  well 
be  contradictory,  but  this  contradiction  is  not  seen  because  no 
attempt  is  made  to  unite  them.  There  is,  of  course,  no  human 
experience  which  is  entirely  systematic,  or  which  has  been  com- 
pletely unified.  Even  those  who  have  thought  most  deeply  find  it 
impossible  to  fit  together  exactly  knowledge  gained  from  different 
fields,  and  from  different  sciences.  The  facts  of  one  science,  for 
example,  may  seem  to  stand  by  themselves,  and  not  to  have  any 
relation  to  the  facts  derived  from  another  science.  Or  there  may 
appear  to  be  a  conflict  between  the  results  of  physical  sciences, 
and  the  truths  of  moral  philosophy  and  religion.  But  the  ideal 
always  remains,  that  truth  is  one  and  indivisible,  and  that  it  must 
be  possible  ultimately  to  harmonize  all  facts  in  one  all-embracing 
system  of  judgments  (cf.  Ch.  XXVI.). 

REFERENCES 

B.  Bosanquet,  The  Essentials  of  Logic,  Lecture  II. 
"  "  Logic,  Vol.  I.,  pp.  97-103. 

C.  Sigwart,  Logic,  §  18. 


CHAPTER   XXIII 

THE    LAWS    OF    THOUGHT 

§  84.  The  Law  of  Identity.  —We  found  (§  78)  that  Judg- 
ment is  the  simplest  form  of  thinking.  And,  in  the  last  chap- 
ter, we  were  engaged  in  studying  its  main  characteristics, 
and  becoming  acquainted  with  its  mode  of  operation.  The 
essential  nature  of  the  thinking  process,  therefore,  has  already 
been  stated,  though  we  have  not  traced  the  mode  of  its  devel- 
opment, or  shown  its  application  to  the  various  problems 
of  experience.  But,  before  undertaking  this,  it  is  necessary 
to  turn  aside  to  consider  another  problem.  In  nearly  all 
books  dealing  with  logic  one  finds  a  statement  of  three  funda- 
mental laws  of  thought  which  differ  greatly,  in  form  at  least, 
from  what  we  have  so  far  learned  regarding  the  nature  of 
Judgment.  These  laws  are  so  well  known  by  name,  and 
yet  so  ambiguous  in  their  mode  of  statement,  that  it  seems 
well  to  try  to  decide  what  meaning  to  apply  to  them.  For 
their  interpretation  will  be  found  to  furnish  further  illustra- 
tion of  the  nature  of  Judgment,  and  will  thus  throw  light  on 
the  discussions  of  the  last  chapter.  The  laws  of  Thought 
are  usually  regarded  as  axioms,  or  propositions  which  require 
no  proof,  rather  than  as  laws  descriptive  of  the  nature  of 
thought  in  any  special  circumstance.  In  this  sense,  they  are 
supposed  to  be  the  foundation  of  all  logic,  since  they  are  pre- 
supposed in  all  thinking. 

The  first  of  these  laws,  or  axiomatic  principles,  is  that  of 
Identity.     '  Whatever  is,  is; '  '  Everything  remains  identical 

343 


344  The  Laws  of  Thought 

with  itself  ; '  '  A  is  A.'  These  are  some  of  the  forms  in  which 
the  law  is  usually  stated.  What  is  meant  by  these  statements 
is,  that  in  all  argument,  we  necessarily  assume,  if  we  are 
to  reason  at  all,  that  each  thing  possesses  a  permanent  char- 
acter, and  does  not  pass  now  into  this,  now  into  that  at  ran- 
dom. If  any  knowledge  is  to  be  possible  at  all,  the  character 
of  things  must  remain  fixed.  Socrates  is  always  to  be  Soc- 
rates, and  iron,  iron.  Things  are  also  constantly  undergoing 
changes.  The  law  of  Identity,  of  course,  does  not  deny  this, 
or  declare  that  the  changes  are  unreal.  It  rather  presupposes 
the  changes;  but  goes  on  to  affirm  that  there  is  an  identity 
persisting  in  and  through  the  difference.  Identity  means 
identity  in  difference:  it  is  this  which  all  our  judgments  as- 
sert. Socrates  changes,  or  is  different  from  day  to  day  and 
from  year  to  year.  But  he  also  remains  identical  with  him- 
self; he  is  in  his  old  age  the  same  Socrates. who  talked  with 
Parmenides  in  his  youth  and  fought  at  Potidaea  when  in 
middle  life.  Identity,  then,  does  not  affirm  the  static  and  un- 
changeable character  of  things  and  thoughts;  but  that 
there  is  continuity  in  change,  in  virtue  of  which  things  main- 
tain themselves  and  are  capable  of  being  known  as  parts  of 
a  coherent  system.  Every  one  assumes  as  much  as  this  in 
every  judgment  he  makes,  though  he  may  not  himself  be 
conscious  of  it  (cf.  §  9). 

Another  interpretation  of  this  principle  was,  however, 
offered  by  Boole  and  Jevons,  who  developed  what  is  known 
as  the  Equational  or  Symbolic  logic.  According  to  these 
writers,  the  law  of  Identity  expresses  the  fundamental  nature 
of  Judgment,  and  is  to  be  interpreted  as  a  statement  of  an 
exact  and  bare  identity.  That  is  to  say,  every  judgment 
is  the  expression  of  an  identity  between  the  subject  and  the 


§  84.    The  Law  of  Identity  345 

predicate.  The  judgment,  '  New  York  is  the  largest  city  in 
America,'  is  simply  a  case  of  a  is  a.  It  expresses  the  fact, 
that  is,  that  New  York  and  the  largest  city  in  America  are 
identical.  '  Iron  is  a  metal,'  is  another  example  of  the  same 
principle.  It  may  be  written:  iron  =  metal.  And,  since 
the  copula  may  often  be  ambiguous,  it  will  be  better  to  discard 
it  in  working  out  arguments,  and  adopt,  in  its  place,  the 
sign  of  equality. 

Judgment,  from  this  point  of  view,  is  thus  simply  an  equation, 
and  may  be  written  as  such.  Furthermore,  the  conclusion 
of  a  series  of  logical  premises  may  be  obtained  by  a  process 
similar  to  that  employed  in  working  algebraic  equations.  That 
is,  we  can  substitute  for  any  term  in  a  judgment,  its  equivalent, 
or  the  value  which  it  has  in  another  judgment.  This  method 
Jevons  calls  '  the  substitution  of  similars,'  which  he  maintains 
is  the  fundamental  principle  of  all  reasoning. 

If,  now,  we  employ  letters  to  symbolize  the  terms  of  the 
propositions,  it  is  claimed  that  we  can  work  out  any  argu- 
ment by  the  equational  method.    Take  the  argument, 

All  metals  are  elements, 

Iron  is  a  metal, 

Therefore  iron  is  an  element. 

Now  represent  metal  by  M,  iron  by  I,  and  element  by  E. 
Then  the  argument  in  equational  form  will  be, 

M  =  E (1) 

I  =  M (2) 

and  by  the  substitution  in  (1)  of  the  value  of  M  in  (2)  we  get 
I  =  E,  the  required  conclusion. 

Or,  we  may  illustrate  this  method  by  a  somewhat  more 
complex  example  which  is  also  taken  from  Jevons:  '  Common 


346  The  Laws  of  Thought 

salt  is  sodium  chloride,  which  is  a  substance  that  crystallizes 
in  cubical  form;  but  what  crystallizes  in  cubical  form  does 
not  possess  the  power  of  double  refraction.'  The  conclusion 
of  this  argument  may  be  found  by  letting  A  =  Common 
Salt,  B  =  Sodium  Chloride,  C  =  something  which  crys- 
tallizes in  cubical  form,  and  D  =  something  which  possesses 
the  power  of  double  refraction.  The  negative  of  any  of  these 
terms  will  be  expressed  by  the  corresponding  small  letters. 
The  argument  may  now  be  expressed :  — 

A  =  B (1) 

B  =  C (2) 

C  =  d (3) 

By  substitution  of  the  value  of  C  in  (2)  we  get, 

B  -  d (4) 

And  substituting  here  the  value  of  B  in  (1), 

A  -  d. 

Giving  to  these  symbols  their  meanings,  we  get  the  result 
'  common  salt  does  not  possess  the  power  of  double  refrac- 
tion,' which  is  the  conclusion  of  the  argument. 

Of  course,  in  simple  arguments  like  those  we  have  been 
examining,  there  is  nothing  gained  by  the  use  of  symbols, 
and  the  representation  of  arguments  in  this  form.  But 
when  the  various  terms  employed  are  much  longer  and  more 
complex,  simplification  may  be  attained  in  this  way.  Va- 
rious other  symbols  have  also  been  used  to  express  the  rela- 
tion of  the  various  terms  to  one  another,  and  a  symbolic 
logic  has  been  developed  which  follows  very  closely  the  pro- 
cedure of  algebra.  By  following  closely  the  methodsof  mathe- 
matics, but  seeking  to  obtain  a  more  general  form  of  express- 
ing the  relations  than   mathematics  employs,  results   have 


§  84.    The  Lazv  of  Identity  347 

"been  obtained  that  are  of  much  interest  and  which  may  prove 
valuable.1 

Tt  is,  however,  as  a  theory  of  the  meaning  of  Judgment  that 
we  are  interested  in  this  mode  of  interpreting  the  law  of 
Identity.  We  have  seen  that  it  works  fairly  well  in  practice, 
and  therefore  cannot  be  wholly  false.  But  there  are  cer- 
tain forms  of  reasoning  in  which  it  will  not  work.  We  can- 
not get  the  conclusion  by  the  equational  method  in  an  example 
like  the  following:  '  B  is  greater  than  A,  C  is  greater  than  B, 
therefore  C  is  still  greater  than  A.' 

This  practical  objection  being  left  out  of  account,  we  have 
to  ask  whether  an  equation  represents  fairly  the  nature  of 
Judgment.  Does  a  judgment  express  merely  the  identity 
of  subject  and  predicate  ?  And  if  so,  what  kind  of  identity 
is  referred  to  ?  In  mathematical  reasoning,  the  sign  of 
equality  expresses  the  identity  of  quantitative  units.  When 
one  says,  2+3  =  5, tne  meaning  is  that  the  number  of  units 
on  each  side  of  the  equation  is  identical.  And,  similarly, 
the  assertion  that  a  parallelogram  =  2  triangles  with  the 
same  base  and  of  the  same  altitude  as  itself,  expresses  the 
fact  that,  in  the  two  cases,  the  number  of  units  of  area,  square 
feet,  square  yards,  etc.,  is  the  same.  In  mathematics,  the 
equation  declares  that  the  quantitative  relations  of  its  two 
sides  are  identical.  It  does  not  assert  that  the  two  things 
compared  —  the  triangle  and  one-half  the  parallelogram, 
for  example  —  have  the  same  qualities,  or  are  exactly  the 
same  in  all  respects.     Now,  if  we  extend  the  use  of  the  sign 

1  The  clearest  statement  of  the  aims  and  methods  of  the  Equational 
Logic  may  perhaps  be  obtained  from  Jevons,  The  Principles  of  Science, 
Introduction.  Cf.  also  G.  Boole,  An  Investigation  of  the  Laws  of  Thought, 
London,  1854;  and  A.  T.  Shearman,  The  Development  of  Symbolic  Logic, 
London,  1906. 


348  The  Laws  of  Thought 

of  equality,  it  must  take  on  a  new  meaning.  It  is  clear  that 
in  a  judgment  like  '  iron  =  metal,'  there  is  no  reference  at 
all  to  quantitative  relations.  We  are  not  asserting  that  the 
number  of  units  in  the  two  terms  is  identical.  What,  then, 
does  the  sign  of  equality  express  in  such  a  case  ? 

The  answer  is  not  difficult,  say  those  who  hold  this  theory. 
The  sign  of  equality  in  such  cases  expresses  absolute  identity; 
the  entire  and  complete  sameness  of  subject  and  predicate. 
The  proposition,  '  mammals  =  vertebrates,'  asserts  that 
mammals  and  vertebrates  are  one  and  the  same  thing.  But 
that  statement  in  its  present  form  is  not  true:  the  class 
mammal  does  not  completely  correspond  with  the  class 
vertebrate.  To  make  it  exact,  reply  those  who  uphold  the 
equational  form,  one  must  qualify  or  limit  the  predicate 
and  write  the  proposition,  '  mammals  =  some  vertebrates.' 
But,  even  so,  we  may  urge,  the  form  of  the  judgment  is  still 
defective.  In  the  first  place,  it  does  not  correspond  to  the 
model  a  =  a.  For  one  side,  '  mammal,'  is  clearly  marked 
off,  while  the  other  is  indefinite  and  vague.  And,  secondly, 
just  because  of  its  vagueness,  it  is  not  a  satisfactory  piece 
of  knowledge.  To  obviate  these  objections,  one  must  go 
further  and  write,  mammals  =  mammalian  vertebrates. 
At  last  the  judgment  seems  to  correspond  to  the  type,  a  =  a. 
But  a  new  difficulty  arises.  Has  not  the  judgment  lost  all 
its  original  meaning  and  become  a  mere  tautology  ?  There 
seems  to  be  no  escape  from  the  following  dilemma:  either 
there  is  some  difference  between  subject  and  predicate,  and 
the  judgment  is  therefore  not  in  the  form  a ',  =  a,  or  the 
judgment  is  tautologous  and  expresses  nothing.  The  view 
of  the  equational  logic  that  Judgment  affirms  the  entire  iden- 
tity of  subject  and  predicate  refutes  itself.    The  form  a  =  a 


§  84-    The  Law  of  Identity  349 

cannot  be  regarded  as  the  type  to  which  all  judgments  con- 
form. 

But  there  must  be  some  kind  of  identity  between  the  parts 
of  a  judgment.  In  one  sense,  we  do  seem  to  declare  that  the 
subject  and  predicate  are  identical  when  we  say,  '  iron  is  a 
metal.'  As  we  have  seen,  however,  if  these  terms  are  merely 
identical  and  nothing  more,  the  judgment  loses  all  meaning. 
We  are  forced  to  the  conclusion  that  every  judgment  affirms 
both  identity  and  difference,  or  that  there  is  identity  running 
through  and  underlying  the  diversity.  But  is  not  this  a 
paradoxical  statement  ?  When  we  affirm  identity,  does  not 
this  imply  the  absence  of  all  difference  ?  If  a  is  a,  how  can 
it  at  the  same  time  be  something  different  from  itself  ? 

And  yet  this  is  just  what  every  judgment  which  has  any 
meaning  affirms.  '  Iron  is  fusible.'  'This  table  is  made  of 
oak.'  '  The  sword  is  rusty  with  age.'  In  all  these  judgments 
there  is  an  assertion  of  the  unity  of  different  properties  or 
parts  in  one  whole.  A  is  B,  and  yet  does  not  cease  to  be  A, 
is  rather  the  type  of  judgment  than  a  is  merely  or  abstractly  a. 
It  is  worth  noticing  that  this  view  of  the  matter  corresponds 
with  the  account  of  Judgment  already  given.  We  saw  that 
Judgment  constructs  a  system  of  knowledge  by  showing 
that  various  things,  which  seem  at  first  unrelated,  are  yet  con- 
nected by  an  underlying  unity.  Knowledge  is  always  the 
synthesis  or  union  of  different  parts  or  different  properties 
in  a  common  identity.  And  each  judgment,  as  an  element  of 
knowledge,  displays  the  same  essential  structure  which  be- 
longs to  knowledge  as  a  whole.  It  involves,  as  was  shown 
in  §  82,  both  analysis  and  synthesis,  and  declares  the  one- 
ness or  identity  of  a  number  of  properties  or  parts,  without 
at  the  same  time  losing  sight  of  their  distinctness. 


350  The  Laws  of  Thought 

Let  us  now  sum  up  our  discussion  of  the  law  of  Identity. 
When  rightly  understood,  as  we  have  seen,  it  does  not  affirm 
that  a  can  only  be  bare  a,  that  the  subject  and  predicate  are 
absolutely  identical.  As  a  law  of  thought,  it  expresses  the 
fact  that  Judgment  brings  together  differences,  i.e.,  different 
things  and  qualities,  and  shows  that  they  are  parts  of  one 
whole  or  unity.  That  is,  judgment  reveals  the  underlying 
unity  or  identity  which  is  present  in  the  midst  of  variety. 
This  law  also  states  another  characteristic  of  Judgment 
which  we  have  already  emphasized.  This  is  what  we  have 
called  the  universality  of  Judgment  (§  80).  It  is  to  judg- 
ments, and  not  to  concepts  or  terms,  as  has  sometimes  been 
supposed,  that  the  law  of  Identity  properly  applies.  What 
it  affirms  in  this  connection  is  simply  that  Judgment  claims 
to  be  true,  and  hence  is  identical  at  all  times  and  for  all  per- 
sons. It  cannot  be  true  for  you  and  false  for  me  that,  '  iron 
is  a  metal,'  and  the  judgment  must  at  bottom  mean  the  same 
for  all  men.  Truth  is  not  a  matter  of  individual  taste,  but 
every  judgment  which  is  true  has  a  permanent  character  or 
identity  of  meaning  belonging  to  it. 

§  85.  The  Law  of  Contradiction.  — The  law  of  Contra- 
diction is  the  second  of  the  so-called  laws  of  thought.  It  is 
usually  stated  as  follows:  it  is  impossible  for  the  same 
thing  both  to  be  a,  and  not  to  be  a,  or,  a  is  not  not-a.  It  is 
evident  that  this  law  states  in  a  negative  form  the  same  char- 
acteristics of  thought  as  the  law  of  identity.  Indeed,  it  was 
in  this  form  that  the  principle  was  first  laid  down  by  Aris- 
totle. "  It  is  impossible,"  he  says,  "  that  the  same  predicate 
can  both  belong  and  not  belong  to  the  same  subject  at  the 
same  time,  and  in  the  same  sense."  '  We  cannot  assert 
1  Metaphysics,  Bk.  III.,  Ch.  IV.     See  also  the  remaining  chapters  of  the 


§  85.    The  Law  of  Contradiction  35 1 

that  Socrates  is  both  wise,  and  not  wise.  Truth  is  not,  as 
the  Sophists  supposed,  a  matter  of  taste  or  convenience,  but 
must  be  consistent  with  itself.  If  a  judgment  affirms  that 
'  iron  is  a  metal,'  it  at  the  same  time  excludes  the  assertion 
that  it  is  not  a  metal.  There  is  a  fixity  and  permanence 
about  judgments  which  prevents  them  from  changing  into 
anything  else.  And  it  is  just  this  permanence  which  we  have 
already  called  the  universality  of  Judgment,  which  the  law 
of  Contradiction  expresses  in  a  negative  form. 

The  law  of  Contradiction  has,  however,  sometimes  been 
interpreted  in  such  a  way  as  to  make  it  equivalent  to  the  as- 
sertion of  abstract  or  bare  identity  which  we  found  in  the 
Equational  logic.  That  is,  the  statement  that  it  is  impossible 
for  any  judgment  to  unite  a  and  not-a  may  be  taken  to  mean 
that  it  is  impossible  to  assert  the  unity  of  a  and  anything 
different  from  a.  But,  as  we  have  seen,  this  is  exactly 
what  we  do  in  every  judgment  which  is  more  than  a  tautol- 
ogy. The  law,  then,  does  not  forbid  the  union  of  differences 
in  one  judgment,  but  of  contradictories,  or  of  what  would 
destroy  the  integrity  of  the  judgment  and  render  it  unmean- 
ing. If  the  law  is  to  hold  true  of  Judgment,  not-a  must  not 
be  taken  as  equivalent  to  anything  which  is  different  from 
a,  but  as  signifying  what  is  opposed  or  contradictory  to  a. 

It  is  not  by  any  means  easy  to  decide  what  things  are  merely 
different,  and  therefore  compatible  with  one  another,  and  what  con- 
tradictory or  opposed.  Logic  can  give  no  rule  which  may  be  applied 
in  every  case.  If  experience  shows  that  two  things,  or  two  proper- 
ties, are  at  any  time  united,  we  say  that  they  are  merely  different 
from  each  other;  if  they  have  never  been  found  in  conjunction  and 

same  book  for  Aristotle's  demonstration  that  all  thought  presupposes  such 
a  principle. 


352  The  Laws  of  Thought 

ve  are  not  able  to  conceive  how  their  union  could  take  place,  we 
call  them  opposites  or  contradictories.  It  is  worth  noticing,  too, 
that  no  terms  are  in  themselves  contradictory,  except  those  which 
are  in  the  form  a  and  not-a,  wise  and  not-wise.  But  they  become 
contradictory  and  exclude  each  other  when  they  claim  to  occupy 
♦he  same  place  in  some  particular  system  of  facts.  Thus  'maple' 
and  '  oak'  denote  trees  of  a  different  variety,  which  are,  however,  so 
little  opposed  that  they  may  exist  side  by  side.  If  both  these  terms 
were  applied  to  the  same  tree,  however,  they  would  become  con- 
tradictory. By  claiming  to  stand  in  the  same  relations,  these 
terms  become  rivals,  as  it  were,  and  exclude  each  other.  But  a 
knowledge  of  the  particular  facts  involved  is  always  necessary  in 
order  to  determine  whether  or  not  two  assertions  are  really  incom- 
patible. 

§  86.  The  Law  of  Excluded  Middle.  —The  third  law  is  a 
corollary  from  what  has  just  been  said  in  the  last  section. 
There  is  no  middle  ground,  it  declares,  between  contradic- 
tories. A  is  either  b  or  nol-b.  To  affirm  the  one  is  to  deny 
the  other.  When  we  have  real  contradictories,  — i.e.,  when 
not-b  is  not  merely  something  different  from  b,  but  some- 
thing which  excludes  it,  —  every  judgment  is  double-edged, 
and  both  affirms  and  denies  at  the  same  time.  To  deny 
that  the  throw  of  a  penny  has  given  heads,  is  to  assert  that 
it  has  fallen  tails.  As  we  have  seen,  however,  logic  affords 
no  rules  for  deciding  when  things  do  thus  stand  in  the  rela- 
tion of  mutual  exclusion.  The  law  of  Excluded  Middle 
states  only  that  -where  this  relation  does  exist,  every  proposi- 
tion has  a  double  value,  and  both  affirms  and  denies  at  the 
same  time.  It  requires  special  knowledge  of  the  particular 
facts  in  each  case  to  enable  us  to  decide  what  things  are 
^hus  opposed  to  one  another.     There   is  no  logical  law  by 


§  86.    The  Law  of  Excluded  Middle  353 

means  of  which  things  may  be  divided  into  two  contradictory 
or  exclusive  groups  or  classes. 

It  is  important  to  notice  that  all  of  the  judgments  which 
we  use  in  everyday  life  are  to  some  extent  double-edged. 
That  is,  they  contain,  besides  what  is  directly  affirmed,  some 
implication  or  counter  statement.  For  example,  to  say, 
'  that  object  is  red,'  is  implicitly  to  deny  that  it  is  blue,  or  any 
other  colour.  The  statement,  '  A  never  looks  at  a  book,' 
carries  with  it  certain  implications  which  may  perhaps  be 
held  in  mind  as  a  series  of  hypotheses:  '  Is  he  then  too  busy, 
or  sick,  or  simply  indifferent  ? '  In  almost  any  field  where 
we  have  any  systematic  knowledge,  we  can  limit  pretty  defi- 
nitely the  number  of  possibilities  —  a  must  be  either  b,  or  c, 
or  d.  In  such  cases,  to  affirm  that  a  is  b,  is  of  course  to  deny 
implicitly  c  and  d;  and  conversely,  the  denial  of  any  one  pos- 
sibility, as  c,  enables  one  to  assert  that  a  is  b  or  d.  In  ordi- 
nary conversation,  misunderstandings  and  misconceptions 
frequently  arise  because  neither  party  is  fully  aware  of  all 
the  possible  cases  and  the  relation  between  them.  It  is  very 
difficult,  however,  to  make  a  statement  which  will  have 
no  counter  implications.  If  one  says,  '  this  railway  system 
does  not  employ  steam  power,'  the  proposition  seems  to  jus- 
tify the  question:  '  Does  it  then  use  electricity  or  compressed 
air  ?  '  We  should  feel  that  it  was  a  mere  quibble  if  the  per- 
son who  made  the  statement  should  reply:  '  I  did  not  say 
it  employed  any  kind  of  power.'  'There  are  some  small 
errors  in  this  paper,'  would  ordinarily  be  taken  to  imply  the 
counter  proposition,  c  the  paper  contains  no  serious  errors.' 
It  is  clear  that  it  is  only  when  one's  knowledge  becomes 
systematic,  — i.e.,  when  one  knows  the  relations  in  which  all 
the  facts  in  the  field  under  consideration  stand  to  one  an- 


354  The  Laws  of  TlwugJit 

other,  —  that  one  can  be  fully  aware  of  what  is  really  implied 
in  each  assertion  or  denial  (cf.  §§  26,  83).  It  is,  however, 
of  fundamental  importance  to  understand  that  in  its  work 
of  defining  the  nature  of  things  thought  works  with  a  double- 
edged  tool.  Omnis  definitio  est  negatio,  wrote  Spinoza:  to 
define  is  to  exclude  or  eliminate.  But  as  we  have  shown, 
the  process  of  elimination  is  not  merely  positive  but  yields 
positive  results. 

These  so-called  Laws  of  Thought,  when  read  in  relation 
to  one  another,  may  then  be  interpreted  as  expressing  the  uni- 
versal Postulate  of  our  intelligence,  that  experience  shall  be 
capable  of  being  organized  as  a  system.  If  there  were 
nothing  but  Identity  —  if  everything  were  identical  with 
everything  else  —  there  could  be  no  universe  and  no  know- 
ledge. Nor  would  any  knowledge  be  possible  if  things  were 
merely  different :  if  there  were  no  common  space  and  time, 
no  common  natures  and  laws  of  relationship,  the  world  would 
be  nothing  but  a  disorganized  chaos,  without  form  and  void. 
Finally,  experience  would  not  be  possible  as  a  coherent  sys- 
tem if  each  fact  had  not  some  particular  place  or  bearing,  in 
such  a  way  that  one  affirmation  or  denial  carried  others  with 
it.  Reality  exists  as  a  system  of  mutual  implications  and 
exclusions.  It  must  so  exist  if  it  is  to  be  knowable.  That 
Reality  is  knowable  by  Intelligence,  may,  then,  be  regarded 
as  the  ultimate  postulate  of  knowledge,  and  this,  as  we  have 
seen,  is  the  final  interpretation  to  be  given  of  the  Laws  of 

Thought. 

REFERENCES 

F.  H.  Bradley,  The  Principles  of  Logic,  pp.  131-154,  343-360. 

B.  Bosanquet,  Logic,  Vol.  II.,  pp.  207-212. 

W.  S.  Jevons,  The  Principles  of  Science,  Introduction. 


CHAPTER  XXIV 

TYPES    OF  JUDGMENT 

§  87.  Judgments  of  Quality.  — We  have  hitherto  been 
considering  the  nature  of  Judgment  in  general,  and  have 
learned  something  regarding  its  main  characteristics.  It  is 
now  necessary  to  examine  briefly  some  of  the  more  important 
forms  or  types  of  Judgment.  In  §  5 1,  we  spoke  of  the  different 
forms  or  conceptions  in  terms  of  which  things  are  brought  into 
relation  as  '  Categories.'  This  chapter  might  therefore  have 
been  entitled,  'The  Main  Categories  of  Thought,'  as  it  is  with 
certain  typical  ways  in  which  things  are  related  that  we  are 
here  concerned.  We  shall  begin  with  very  simple  and  elemen- 
tary ways  of  judging,  and  afterwards  consider  some  of  the 
more  complex  types.  In  this  way,  we  shall  see  the  nature 
and  structure  of  Judgment  illustrated  at  different  levels  of 
thought.  We  also  hope  to  show,  by  this  review  of  types, 
that  there  are  no  arbitrary  divisions  in  the  process  of  thinking, 
but  that  the  lower  forms  of  Judgment  gradually  develop  into 
the  higher  in  accordance  with  the  general  law  of  evolution. 
It  is,  of  course,  impossible  to  carry  out  at  present  this  plan  in 
detail,  for  that  would  be  to  give  a  complete  history  of  the 
development  of  thought.  It  will  be  necessary  for  us  to  take 
long  steps,  and  content  ourselves  with  a  general  view  of  the 
relation  of  the  various  stages  in  the  development  of  Judgment. 

The  first  efforts  of  intelligence  to  understand  the  world 
take  the  form  of  judgments  of  Quality.     At  a  low  stage  of 


^6  Types  of  Judgment 

mental  development,  it  is  the  simple  qualities  of  things 
which  force  themselves  on  attention.  The  young  child,  for 
example,  takes  notice  only  of  the  most  striking  qualities  of 
things.  His  judgments  are  very  vague  and  indefinite,  and 
take  account  only  of  some  prominent  quality  of  things.  That 
is,  there  is  in  them  no  discrimination  of  the  various  parts  and 
relations  of  the  objects,  but  they  express  merely  a  general 
impression  based  upon  some  striking  quality.  Thus  it  has 
often  been  noticed  that  the  child  calls  every  man  '  papa,' 
and  any  light,  of  whatever  size,  the  moon.  A  little  boy, 
known  to  the  author,  used  to  call  Sisters  of  Charity  crows,  on 
account  of  the  colour  of  their  dresses.  The  objects  as  he 
apprehended  them  were  simply  black,  and  nothing  more. 
His  intelligence  rested  in  the  qualitative  total  impression: 
the  various  parts,  with  their  diverse  relations,  which  he 
afterwards  learned  to  know  and  distinguish,  did  not  at  that 
time  exist  for  him. 

It  is  perhaps  impossible  to  find  in  the  experience  of  an 
adult  any  judgments  which  deal  entirely  with  simple  qualities, 
and  which  take  no  account  of  the  numbers,  or  even  to  some 
extent  of  the  relations,  of  the  parts.  But  we  can  find  examples 
of  judgment  where  the  qualitative  aspect  is  much  the  most 
prominent — where  indeed  the  quantitative  and  more  com- 
plex relations  are  scarcely  noticed  at  all.  'This  is  green,' '  that 
is  a  strange  odour,'  '  there  is  something  a  lmg  way  off,'  — 
all  these  seem  to  be  judgments  of  quality  or  general  impres- 
sion, and  to  involve  scarcely  any  other  element.  This  is, 
also,  the  easiest  kind  of  judgment  to  make,  the  judgment  which 
involves  least  mental  effort,  and  which  notices  only  the  most 
evident,  and,  as  may  be  seen,  the  most  superficial,  aspect  of 
things.     It  is  evident  that  such  judgments  belong  to  a  lower 


§  8y.  Judgments  of  Quality  357 

stage  of  thinking  than  those  which  imply  analysis  and  per- 
ception of  quantitative  relations.  Compare,  for  example, 
'  this  is  very  large,'  with,  '  this  tree  is  made  up  of  roots,  trunk, 
branches,  and  leaves';  or  'this  is  green,'  with,  'this  leaf 
is  divided  into  two  parts  by  a  rib  running  through  the  centre.' 
The  first  judgment  in  each  pair  obviously  involves  much  less 
intellectual  work  than  the  latter.  The  judgment  of  simple 
quality  accordingly  is,  as  we  have  said,  the  starting-point  of 
thought.  It  is  with  this  kind  of  thinking  that  the  knowledge 
of  the  child  begins.  And,  before  the  savage  learns  to  count, 
i.e.  to  distinguish  and  enumerate  the  parts  of  the  objects  with 
which  he  deals,  his  judgments  must  necessarily  belong  to  this 
same  type. 

It  must  never  be  forgotten,  however,  that  simple  judgments 
of  quality  are  really  judgments;  that  is,  they  are  not  given  to 
the  mind  from  any  external  source,  but  are  the  products  of 
its  own  activity.  A  judgment,  as  we  have  already  pointed 
out  (§  78),  implies  a  reaction  on  the  part  of  the  mind  on  what 
is  presented  to  consciousness  through  the  senses.  It  dis- 
tinguishes and  puts  together  the  material  which  sense  pre- 
sents in  such  a  way  as  to  perceive  its  significance  —  what  it 
really  amounts  to  —  as  a  piece  of  knowledge.  This  act  of 
interpretative  intelligence  has  gone,  however,  but  a  little 
way  in  the  type  of  judgment  with  which  we  are  dealing. 
But  even  in  a  vague  qualitative  judgment  like, '  there  is  some- 
thing black,'  the  essential  characteristics  of  Judgment  can  be 
already  distinguished.  For  it  presupposes  at  least  some 
analysis  or  discrimination  of  the  black  object  from  the  rest  of 
the  environment,  and  of  the  black  colour  from  other  colours. 
And  the  judgment,  'something  is  black,'  has  made  at 
the  same  time  a  beginning  in  constructing  this  vague  some- 


358  Types  of  Judgment 

thing  into  a  system  of  qualities,  or  into  a  thing  that  is  known 
The  other  qualities  and  relations  are  as  yet  wrapped  up  in  the 
indefiniteness  of  the  'something.'  In  spite  of  its  indefinite- 
ness,  however,  the  latter  plays  the  part  of  a  permanent  centre 
or  identity.  It  is  the  whole  from  which  the  quality  of  black- 
ness has  been  separated  out,  and  to  which  it  is  again  attached. 

Our  thought,  however,  is  not  satisfied  with  a  knowledge  of 
the  general  qualities  of  things,  but  pushes  farther  its  work  of 
analysis  and  construction.  In  this  way,  it  begins  to  distin- 
guish the  various  parts  of  objects,  and  to  compare  one  with  an- 
other. We  not  only  judge  that  'the  grass  is  green,'  but  go 
further  and  say  '  this  piece  is  dark  green,  and  that  light  green.' 
The  indefinite  judgment,  'this  cane  is  heavy,'  is  no  longer 
satisfactory,  and  is  replaced  by,  '  this  end  of  the  cane  is  much 
heavier  than  that.'  And  when  this  stage  is  reached,  judg- 
ments of  Quality  are  already  passing  into  the  next  higher 
type,  judgments  of  Quantity.  For  the  element  of  comparison, 
which  is  already  contained  in  these  judgments,  is  the  basis  of 
counting,  measuring,  and  all  quantitative  determination.  In 
advancing  from  the  simple  apprehension  of  quality,  to  the 
stage  where  it  takes  note  of,  and  compares,  the  degree  or 
intensity  which  the  same  quality  manifests  in  different  instances, 
intelligence  has  entered  upon  a  path  which  leads  directly  to 
judgments  of  quantity.  To  distinguish  parts,  to  regard  things 
as  degrees  or  instances  of  a  common  quality,  is  at  once 
to  suggest  the  quantitative  process  of  counting  and  measure- 
ment. 

§  88.  Judgments  of  Quantity.  —  It  is  very  difficult,  as  we 
have  seen,  to  draw  a  hard  and  fast  line  between  quality  and 
quantity.  Indefinite  judgments  of  general  impression  which 
do  not  imply  any  comparison,  seem  always  to  be  qualitative 


§  88.  Judgments  of  Quantity  359 

rather  than  quantitative  in  character.  This  is  true,  I  think, 
of  judgments  like, '  this  object  is  very  large,' '  there  was  a  great 
flock  of  sheep  in  the  field.'  In  such  cases,  the  interest  does 
not  seem  to  be  quantitative  at  all;  i.e.  there  is  no  effort 
made  to  determine  how  many  units  or  parts  there  are  in  the 
whole  about  which  the  judgment  is  made.  But  the  general 
impression  of  size  or  number  is  apprehended  and  judged  of 
at  the  same  level  of  intelligence,  and  in  the  same  vague  way, 
as  the  simple  qualities  with  which  we  dealt  in  the  last  section. 
It  is  by  means  of  such  a  general  qualitative  impression  that 
the  savage  who  cannot  count  beyond  five,  is  able  to  distinguish 
between  six  and  some  larger  number.  And  we  cannot  im- 
agine that  the  shepherd's  dog  learns  that  some  of  the  sheep  are 
missing  by  any  process  of  counting.  We  must  suppose  that 
the  general  qualitative  impression  made  by  the  smaller  flock 
is  different  from  that  made  by  the  larger,  and  that  there  has 
been  no  real  counting  or  estimation  of  number  in  the  case. 

But  quantitative  judgments  proper  belong  to  a  higher  stage 
of  intelligence  than  do  those  which  have  just  been  described. 
Indefinite  judgments,  like  '  this  is  very  large,'  or,  '  there  are  a 
great  many  stars  in  that  group,'  are  not  satisfactory  pieces  of 
knowledge.  We  accordingly  set  ourselves  to  get  more  exact 
information  about  the  parts  which  compose  the  wholes,  or  to 
analyze  and  distinguish.  The  first  step  in  this  process  leads 
to  Judgments  of  Enumeration.  If  the  whole  which  is  analyzed 
is  composed  of  homogeneous  parts,  the  judgments  of  enumera- 
tion take  the  form  of  simple  counting.  'There  are  one,  two, 
three,  .  .  .  twenty  men  in  this  company.'  Where  the  parts 
are  not  of  the  same  kind,  however,  a  separate  name  may 
have  to  be  given  to  each.  'This  plant  is  composed  of  root, 
stalk,  leaves,  and  flower.' 


360  Types  of  Judgment 

But  exact  quantitative  knowledge  requires  us  to  do  more 
than  enumerate  the  parts  of  which  a  whole  is  composed.  We 
must  go  on  and  weigh  or  measure  them.  There  is  of  course  no 
essential  difference  between  weighing  and  measuring,  so  that 
we  may  call  all  judgments  which  express  the  result  of  this 
process  Judgments  of  Measure.  It  is  worth  noting  that  judg- 
ments of  this  class  are  not  so  simple  and  direct  as  may  ap- 
pear at  first  sight.  When  we  measure,  we  express  the  relation 
of  the  parts  with  which  we  are  dealing  to  some  common  unit 
or  standard.  The  judgment,  'this  tower  is  200  feet  high,' 
means  that  if  the  tower  is  compared  with  a  foot-rule,  it  will  be 
found  to  be  200  times  as  long.  It  really,  then,  involves  a  pro- 
portion, and  might  be  expressed:  — tower  :  foot-rule  =  200  : 1. 

The  point  which  it  is  important  to  notice  is  that  all  measure- 
ment is  the  result  of  comparison.  In  the  first  place,  some  unit 
is  more  or  less  arbitrarily  selected.  Then  the  judgment  states 
simply  the  relation  between  this  unit  and  the  object  measured: 
one  is  contained  in  the  other  once,  or  twice,  or  ten  times. 
The  quantitative  determination  thus  obtained  is  accordingly 
merely  relative.  That  is,  it  does  not  belong  absolutely,  and 
in  its  own  right  to  the  object  measured,  hut  indicates  the  rela- 
tion of  that  object  to  something  else. 

For  this  reason,  it  may  seem  that  quantitative  relations 
tell  us  nothing  regarding  the  real  nature  of  objects,  and  that 
to  discover  what  the  latter  are  in  themselves,  we  shall  have  to 
return  to  the  point  of  view  of  quality.  But  we  have  seen  that 
simple  judgments  of  quality  yield  a  very  vague  and  unsatis- 
factory kind  of  knowledge.  Moreover,  we  should  discover, 
by  thinking  the  matter  out,  that  even  qualities  always  imply 
a  reference  to  one  another,  and  are  no  more  absolute  than 
quantities. 


§  88.  Judgment  of  Quantity  361 

In  order  to  obtain  more  satisfactory  knowledge  regarding 
things,  we  shall  have  to  go  forward  to  a  higher  type  of  judg- 
ment, rather  than  backward  to  quality.  But  the  importance 
of  quantitative  determination  for  exact  knowledge  must  not 
be  overlooked.  By  means  of  measurement,  things  are  re- 
duced to  common  terms,  as  it  were,  and  thus  a  basis  cf  com- 
parison is  afforded  where  it  would  otherwise  be  impossible. 
To  reduce  everything  to  such  a  common  measure  is  the  busi- 
ness of  the  physico-mathematical  sciences.  Everything  has 
a  quantitative  value,  and  can  be  expressed  mathematically  in 
terms  of  some  unit  or  standard,  as,  for  example,  the  unit  of 
heat,  or  of  pressure,  or  the  electrical  unit.  It  was  this  ten- 
dency to  count  and  measure  and  weigh  things  which  es- 
tablished the  body  of  exact  knowledge  which  we  call  science. 
And  in  almost  every  field,  knowledge  increases  greatly,  both 
in  extent  and  exactness,  as  soon  as  it  is  found  possible  to  re- 
duce the  phenomena  under  investigation  to  a  common  measure, 
and  to  express  their  relations  by  means  of  mathematical 
formulas. 

It  is  a  great  step  in  advance  to  be  able  to  compare  things  as 
quantities,  and  to  express  their  relations  in  terms  of  number.  But 
judgments  of  quantity  are  not  entirely  satisfactory ;  they  are,  as  has 
already  been  noticed,  merely  relative  in  character.  Moreover,  from 
a  quantitative  point  of  view,  each  thing  is  equivalent  to  the  sum  of 
its  parts.  When  the  parts  have  been  enumerated  and  measured, 
the  value  of  the  whole  is  obtained  by  addition.  But  it  is  scarcely 
ever  possible  to  represent  adequately  the  nature  of  a  whole  in  this 
way.  So  long  as  we  are  dealing  with  a  piece  of  inorganic  matter, 
the  method  of  regarding  the  sum  of  the  parts  as  equivalent  to  the 
thing,  generally  gives  good  results  and  leads  to  no  difficulty.  But  it 
is  quite  different  when  the  whole  question  belongs  to  something 
which  has  life  and  consciousness.     In  such  cases,  we  have  what  has 


362  Types  of  Judgment 

already  been  called  an  organic  whole  (§  83).  Now,  it  is  clear  thai 
the  principle  of  quantity,  which  can  only  add  and  subtract,  is  in- 
sufficient to  represent  completely  the  nature  of  an  object  of  this  kind. 
It  has  no  means  of  representing  the  individuality  or  real  whole, 
which  rather  constitutes  the  parts,  than  is  constituted  by  them. 
That  is,  to  understand  such  objects,  we  shall  have  to  take  a  new 
point  of  view,  and  begin  with  the  whole  rather  than  with  the  parts. 
From  the  point  of  view  of  quantity,  the  nature  of  the  whole  is  dis- 
covered by  adding  together  the  parts ;  while  in  objects  which  possess 
an  individuality  of  their  own,  there  seems  to  be  a  central  principle 
to  which  the  parts  are  subordinated,  and  in  relation  to  which  alone 
they  can  be  understood.  The  type  of  judgments  which  deal  with 
such  objects  we  shall  have  to  discuss  in  §  90. 

§  89.  Judgments  of  Causal  Connection.  —  Another  class  of 
judgments  used  in  building  up  knowledge,  may  be  called 
judgments  of  Causal  Connection.  They  undertake  to  show 
how  the  various  changes  which  go  on  in  things  are  connected 
causally  with  other  things  or  events.  This  type  of  judgment 
—  leading  as  it  does  beyond  the  particular  object  to  a  know- 
ledge of  the  ways  in  which  objects  are  connected  —  seems 
to  belong  to  a  higher  stage  of  mental  development  than  those 
which  merely  take  note  of  quality  and  quantity.  This  does 
not  mean  that  we  never  look  for  causes  until  the  qualities  and 
quantities  of  things  have  been  discovered.  Nor  is  it  true  that 
any  causal  judgment,  however  vague  and  unsatisfactory,  is 
higher  than  any  judgment  of  quality  or  quantity  whatsoever. 
But,  in  the  beginnings  of  knowledge,  one  may  say,  thought 
does  not  travel  outside  the  particular  object  to  show  the  con- 
nections of  the  latter  with  anything  else.  And,  beginning  in 
this  way,  it  seizes  first  upon  quality  and  quantity;  which  seem 
to  belong  to  things  in  themselves.  We  have  seen,  however, 
that  as  a  matter  of  fact  judgments  of  quantity  involve  com- 


§  89»  Judgments  of  Causal  Connection  363 

parison,  and  so  a  reference  of  one  thing  to  another,  though 
that  reference  is  not  usually  made  consciously  or  explicitly. 
In  this  form  of  judgment,  the  reference  does  not  seem  to 
imply  any  objective  relations  of  the  things  compared.  If,  for 
example,  I  say  that  this  desk  is  twice  as  long  as  my  arm,  this 
relation  appears  quite  external  and  accidental:  the  nature  of 
the  one  remains  independent  of  that  of  the  other.  But, 
when  we  judge  that  one  thing  is  causally  connected  with  an- 
other, the  accidental  relation  expressed  in  quantity  has  be- 
come essential  and  objective,  indicating  a  closer  relation- 
ship between  things  than  is  expressed  in  a  quantitative 
comparison  of  the  judgment. 

The  word  '  cause '  has  been  used  in  a  great  many  senses, 
and  its  various  meanings  have  given  rise  to  a  great  deal  of 
discussion.  That  every  event  must  have  a  cause,  was  for- 
merly regarded  as  an  innate  truth,  or  a  priori  proposition. 
We  have  seen,  however,  that  we  do  not  come  into  the  world 
with  any  ready-made  stock  of  knowledge.  All  knowledge,  we 
have  often  repeated,  is  the  result  of  the  mind's  own  judging 
activity.  The  so-called  law  of  causation  (every  event  must 
have  a  cause)  must  therefore  express  the  fact  that  thought 
does  connect  things  as  causes  and  effects.  Intelligence  is  not 
satisfied  to  take  things  in  isolation;  it  tries  to  gain  an  insight 
into  the  ways  in  which  they  are  connected,  to  discover  what  one 
has  to  do  with  another.  And  this  is  just  the  characteristic  of 
thought  which  was  emphasized  in  §  83.  Judgment,  it  was 
there  said,  is  a  process  of  constructing  a  system,  of  showing  how 
the  various  parts  of  knowledge  fit  into  one  another,  and  are 
mutually  dependent  upon  one  another.  The  tendency  of 
thought  to  connect  things  causally,  then,  is  simply  one  of  the 
fundamental  forms  in  which  its  tendency  towards  a  system 


364  Types  of  Judgment 

expresses  itself.  In  employing  the  causal  category,  judgment 
has  become  more  explicit  and  conscious  of  itself  than  it  was 
>n  quality  and  quantity. 

It  is  interesting  to  note  some  of  the  more  important 
changes  which  take  place  in  the  principle  of  causal  explana- 
tion at  different  stages  in  the  development  of  knowledge. 
The  child  and  the  savage  regard  all  changes  and  events  which 
take  place  in  the  natural  world,  as  due  to  the  agency  of  living 
beings.  These  beings  are  represented  as  more  or  less  similar 
to  men,  and  as  endowed  with  human  passions  and  emotions. 
Thus  we  say  that  the  earliest  kind  of  explanation  is  essentially 
anthropomorphic.  This  word  is  derived  from  avdpco7ro<;,  a 
man,  and  popcprj,  shape  or  form,  and  hence  is  used  to  describe 
the  way  of  representing  either  a  spiritual  being,  as,  for  example, 
the  Deity,  or  natural  forces  like  fire,  wind,  etc.,  in  human 
form.  It  is  probably  true  that  at  a  very  early  stage  in  the 
development  of  both  the  individual  and  the  race,  every  object 
was  supposed  to  have  life.  Or,  perhaps,  it  would  be  truer  to 
say  that  the  young  child  (and  the  same  would  be  true  for  the 
savage  on  a  low  plane  of  intelligence)  has  not  yet  made  the 
distinction  between  animate  and  inanimate  objects,  but 
vaguely  regards  everything  as  like  himself.  This  stage  is 
usually  known  as  animism,  because  each  object  is  supposed 
to  be  endowed  with  a  spirit,  or  anima. 

Gradually,  however,  the  distinction  between  animate  and 
inanimate  objects  becomes  clear.  Accordingly,  we  find 
that  at  a  somewhat  more  advanced  stage  the  mode  of  explana- 
tion takes  a  different  form,  though  it  is  still  anthropomorphic. 
Physical  objects  are  no  longer  regarded  as  having  life  in 
themselves;  the  changes  in  them  are  supposed  to  be  due  to 
the  action  of  spirits,  who  are  separate  from  the  objects,  but 


§  89-  Judgments  of  Causal  Connection  365 

who  use  them  to  accomplish  their  purposes.  These  invisible 
spiritual  agents,  to  whom  all  natural  events  are  referred,  have 
been  variously  named.  It  is  clear,  however,  that  the  gods 
of  mythology  belong  here,  as  well  as  the  fairies,  elves,  ghosts 
and  witches  of  the  popular  folk  stories.  It  was  a  great  ad- 
vance when  a  Greek  thinker,  named  Thales,  came  to  the 
conclusion  that  it  does  not  in  any  way  explain  natural  events 
to  refer  them  to  the  action  of  the  gods.  For,  in  the  first  place, 
to  say  that  the  gods  cause  this  or  that  event,  is  to  state  some- 
thing which  we  have  no  means  of  proving.  And,  even  if  the 
assertion  were  true,  it  would  not  really  explain  anything. 
For  it  would  not  enable  us  to  understand  how  the  changes  in 
question  came  about.  It  would  tell  nothing  whatever  re- 
garding the  actual  steps  in  the  process  itself.  Thales  saw  this, 
and  tried  to  give  a  natural  explanation  of  the  world,  and  all 
that  goes  on  in  it.  He  tried  to  build  up  a  real  system  of  know- 
ledge by  attempting  to  show  how  everything  which  has 
happened  in  the  world  has  been  connected  -with  some  natural 
cause.  We  know  very  little  about  the  actual  explanation  of 
the  world  which  Thales  gave,  except  that  he  tried  to  derive 
everything  from  water.  It  is  on  account  of  the  method  which 
he  adopted,  rather  than  of  what  he  actually  performed,  that  he 
is  regarded  as  the  founder  of  science.  Thales  first  showed, 
one  may  say,  that  knowledge  means  an  insight  into  the  ways 
in  which  the  actual  phenomena  of  the  world  are  connected  with 
one  another.  We  cannot  unite  into  a  system  things  so  differ- 
ent in  kind  as  spirits  and  natural  phenomena.  Or  we  may 
say  that  real  explanation  demands  that  there  shall  be  some 
likeness,  or  ground  of  similarity,  between  the  cause  and  the 
effect.  An  event  which  happens  in  the  world  of  objects 
must  be  explained  by  showing  its  connection  with  some 
other  event,  of  a  similar  character,  on  which  it  depends. 


366  Types  of  Judgment 

The  development  of  this  conception  of  scientific  explanation 
also  influenced  still  further  the  notion  of  causality.  We  have 
seen  that  in  the  beginnings  of  knowledge  every  event  was 
supposed  to  be  due  to  the  action  of  some  living  agent,  or 
spiritual  being.  Even  after  this  mythological  mode  of  expla- 
nation is  discarded,  and  natural  causes  put  in  the  place  of 
spirits,  it  is  still  difficult  to  rid  oneself  entirely  of  the  old 
anthropomorphism.  The  popular  mind  still  tends  to  regard 
the  cause  as  an  agent  which  produces  the  effect,  through 
some  power  or  efficiency  which  it  possesses.  It  is  not  neces- 
sary to  raise  the  question  at  present  whether  there  are  any 
grounds  for  this  belief.  To  discuss  this  problem  would  carry 
us  beyond  logic  into  metaphysics.  What  we  wish  to  notice  is 
that  science  has  gradually  abandoned  the  notion  that  the 
cause  does  something  to  the  effect.  That,  as  we  have  seen,  is  a 
remnant  of  the  old  pre-scientific  idea,  and  a  notion  which 
does  not  aid  at  all  in  explaining  phenomena.  It  is  the  business 
of  science  to  show  how  the  things  and  events  which  make  up 
our  experiences  are  necessarily  connected  with  one  another. 
Science  has  to  discover  what  things  invariably  go  along  with 
one  another,  and  necessarily  presuppose  one  another.  And, 
when  it  is  found  that  some  particular  thing  or  event,  A,  is 
invariably  necessary  for  the  appearance  of  another  particular 
occurrence,  B,  the  former  is  regarded  as  the  cause,  and  the 
latter  as  the  effect.  In  order  to  eliminate  as  far  as  possible 
the  notion  of  agency  or  efficiency  which  attaches  to  the  word 
cause,  the  terms '  antecedent '  and  '  consequent '  are  often  used 
to  indicate  this  relation.  For  science,  the  cause  is  not  an 
active  agent,  but  the  invariable  and  necessary  antecedent  of 
something  else  which  simply  follows  it.  The  cause  does  not 
explain  the  effect  by  assigning  an  agent  which  brings  the 


§  %9'  Judgments  of  Causal  Connection  367 

/atter  about  through  its  personal  efforts;  but  it  explains,  be- 
cause it  reveals  another  necessary  step  in  the  process,  and 
gives  us  a  new  fact  which  joins  on  or  can  be  connected  with 
the  one  from  which  we  start. 

We  conclude  then  that  the  cause  of  any  event  is  its  invari- 
able and  necessary  antecedent.  It  has  been  already  explained, 
however,  (p.  237)  that  by  antecedent  is  not  meant  merely 
that  which  is  prior  to  the  effect  in  time.  The  word  must 
be  understood  as  signifying  the  essential  condition  or  what  is 
1  logically '  prior.  Temporal  priority  is  often  taken  practically 
as  an  indication  of  logical  priority,  but  the  two  relations  can- 
not be  identified.  In  another  part  of  this  book  (Chs.  XVL, 
XVII.),  it  is  shown  what  tests  it  is  necessary  to  apply  in 
order  to  determine  whether  two  phenomena  are  merely 
accidentally  conjoined,  or  whether  the  connection  is  essential 
and  real.  It  is  necessary  now  to  take  one  more  step  in  tracing 
the  various  ways  in  which  the  idea  of  causality  has  been  used. 
As  a  result  of  a  famous  scientific  discovery,  which  was  made 
a,bout  the  middle  of  the  preceding  century,  a  new  element 
has  been  added  to  the  notion  of  cause  in  its  application  to 
physical  phenomena.  The  law  of  the  Conservation  of  Energy 
states  that  the  amount  of  energy,  or  power  of  doing  work, 
possessed  by  any  set  of  bodies,  regarded  as  a  closed  mechani- 
cal system,  remains  constant.  Any  change  in  a  material  body 
is  the  result  of  a  transformation  of  energy  from  one  form  to 
another.  The  same  notion  is  applied  to  the  world  as  a  whole : 
it  is  assumed  that  the  total  amount  of  energy  which  it  con- 
tains remains  constant.  All  changes  which  take  place  in  the 
physical  universe  — motion  into  heat,  or  electricity  into  mo- 
tion —  are  regarded  as  simply  different  forms,  or  manifesta- 
tions, of  the  one  world-energy. 


368  Types  of  Judgment 

As  a  result  of  this  law,  the  effect  always  represents  the  same 
amount  of  energy,  or  power  of  doing  work,  as  the  cause. 
Since  no  energy  is  ever  lost,  the  one  must  be  equal  to  the 
other.  And,  as  a  matter  of  fact,  the  quantitative  equivalence 
of  many  of  the  various  forms  of  energy  has  been  proved  by 
actual  measurement.  In  working  out  this  law,  for  example, 
Joule  showed  that  "  the  energy  stored  up  in  the  i-lb.  weight 
which  had  been  pulled  up  772  feet  was  gradually  transformed, 
as  soon  as  the  weight  was  released,  into  an  amount  of  heat 
capable  of  raising  the  temperature  of  a  pound  of  water  i°  Fahr. ; 
while  Hirn  showed,  on  the  other  hand,  that  exactly  this 
amount  of  heat  would,  if  it  could  be  turned  back  again  into 
energy,  raise  the  i-lb.  weight  to  the  height  of  772  feet  at  which 
it  stood  before."  ' 

The  new  element  which  this  law  adds  to  the  idea  of  cause  as 
a  necessary  and  invariable  antecedent,  is  that  of  the  quanti- 
tative identity  of  cause  and  effect.  Taking  the  phenomena 
which  are  connected  in  this  way  to  represent  simply  certain 
quantities  of  energy,  we  say  that  the  one  is  equivalent  to  the 
other.  The  energy  which  the  cause  represents  has  been 
transformed  without  loss,  and  reappears  in  the  effect.  If 
what  seems  to  be  the  total  effect  is  not  equal  to  the  cause,  part 
of  the  energy  of  the  latter  must  have  been  transformed  into 
something  else  as  yet  perhaps  unnoticed.  No  energy  can 
have  been  lost. 

It  becomes,  therefore,  the  task  of  the  physical  sciences  to 
show  that  this  relation  of  quantitative  identity  exists  between 
phenomena  which  are  causally  connected  when  these  are  re- 
garded by  the  science  as  constituting  a  closed  mechanical 
system.    The  ideal  of  physical  science  is  to  prove  that  two 

1  Buckley,  Short  History  of  Natural  Science,  p.  339. 


§  89.  Judgments  of  Causal  Conttection  369 

groups  of  phenomena  are  connected  as  cause  and  effect,  by 
showing  that  both  represent  the  same  quantity  of  energy.  For 
this  purpose,  measurement  and  calculation  are  necessary. 
The  physical  sciences,  as  was  pointed  out  in  the  last  section, 
deal  largely  with  judgments  of  quantity,  and  devote  them- 
selves to  showing  by  measurement  that  the  same  amount  of 
energy  persists  through  the  various  changes  which  phenomena 
undergo.  In  establishing  causal  connections,  therefore,  the 
physical  sciences  find  it  necessary  to  use  the  principles  of 
measurement  and  calculation. 

It  will  be  evident,  from  what  has  been  already  stated,  that  this 
relation  of  cause  and  effect  should ,  in  theory,  apply  to  all  phenomena 
whose  energy  is  capable  of  being  measured  and  represented  in 
quantitative  terms.  As  a  matter  of  fact,  however,  the  law  has  been 
proved  only  in  physics  and  chemistry.  From  the  very  nature  of 
the  case,  it  is  extremely  difficult  to  measure  exactly  the  relations 
of  cause  and  effect  in  the  sciences  which  deal  with  organic  life. 
But  even  in  those  sciences,  the  law  of  the  Conservation  of  Energy 
is  assumed  to  hold  true.  For  example,  the  amount  of  energy 
which  a  plant  contains,  is  assumed  to  be  exactly  the  same  as  that 
represented  by  the  various  elements  or  forces  —  water,  sunlight, 
mineral  substances,  etc.  —  which  were  instrumental  in  composing 
it.  In  the  same  way,  we  suppose  that  the  same  relation  holds  of 
the  changes  which  go  on  in  the  brain,  though  we  are,  of  course, 
unable  to  prove  this  by  actual  measurement.  We  may  accordingly 
speak  of  the  law  of  the  Conservation  of  Energy  as  the  working 
postulate  of  these  sciences. 

It  is  difficult,  however,  to  see  how  this  law  can  have  any  applica- 
tion to  mental  phenomena.  We  can  indeed  measure  the  intensity 
and  duration  of  sensations.  But  neither  feelings  nor  complex 
processes  of  mind  seem  to  be  capable  of  measurement  in  fixed  and 
unambiguous  units.     Moreover,  it  is  never  possible  to  measure 


370  Types  of  Judgment 

the  energy,  or  power  of  doing  work,  which  states  of  consciousness 
possess,  and  to  equate  one  with  another  in  this  respect.  And  this 
being  so,  the  law  of  the  Conservation  of  Energy  cannot,  of  course, 
apply  to  psychical  causes  and  effects.  In  the  mental  sciences, 
then,  we  cannot  claim  that  the  notion  of  Causality  contains  the 
element  of  quantitative  identity  between  cause  and  effect  which 
has  been  found  to  exist  in  the  physical  sciences.1 

§  90.  Judgments  of  Individuality.  —  By  Judgments  of 
Individuality,  we  mean  judgments  which  regard  some 
complex  object  as  a  real  whole  with  a  definite  nature  of  its 
own.  Judgments  of  this  kind  are  also  frequently  called 
Judgments  of  Purpose,  or  Teleology.  We  have  already  had 
occasion  (§  83)  to  distinguish  a  mere  aggregate  or  sum  of 
parts,  like  a  heap  of  stones,  from  a  true  whole  which  pos- 
sesses a  certain  character  and  individuality  of  its  own.  It  is 
as  aggregates  rather  than  as  true  wholes  that  judgments  of 
quantity  and  of  causal  connection  regard  objects.  For  these 
types  of  judgments  are  concerned  with  the  parts  —  the 
former  to  measure  them,  and  the  latter  to  show  their  causal 
connection.  It  requires  a  new  form  of  judgment  to  represent 
adequately  the  nature  of  a  complex  object  which  possesses 
individuality.  This  form  gives  expression  to  the  organic  unity 
and  wholeness  of  things,  and  emphasizes  the  way  in  which 
the  parts  cooperate  for  a  common  purpose  or  end.  Thus  we 
regard  the  parts  of  a  plant  as  a  unity  cooperating  in  a  common 
purpose,  and  a  man  as  a  conscious  system  of  ends.  The 
question  as  to  whether  it  is  allowable  to  employ  any  other 
category,  or  form  of  explanation,  in  science  than  that  of  cau- 
sality, is  of  great  importance.  In  biology,  for  example, 
it  is  usual  to  explain  certain  structures  of  plants  and  animals 
1  Cf.  Wundt,  Ethik  (1st  ed.),  pp.  398  f.;    Sigwart,  Logic,  §  97  a,  7. 


§  9°-  Judgments  of  Individuality  371 

as  purposive.    How  far,  now,  is  it  allowable  to  go  in  substitut 
ing  this  teleological  form  of  explanation  for  explanation  in 
causal  terms  ?     This  question  is  too   large  to  be  discussed 
here,  but  it  is  suggested  as  of  fundamental  importance  both 
for  science  and  philosophy. 

(1)  We  have  seen  that  judgments  of  causal  connection  relate 
phenomena  as  causes  and  effects.  A  change  in  an  object  is  ex- 
plained by  showing  that  some  other  change  or  event  invariably  pre- 
cedes it.  But  this  change,  in  its  turn,  demands  explanation,  and 
has  to  be  accounted  for  by  the  discovery  of  a  new  cause.  This 
type  of  judgment  shows  that  one  phenomenon  is  connected  with 
a  second,  a  second  with  a  third,  and  so  on  indefinitely.  The 
view  of  the  world  which  it  presents  is  that  of  a  never-ending  series 
of  causes  and  effects.  It  is  never  possible  to  find  a  cause  which  is 
not  itself  the  effect  of  something  else.  No  phenomenon  possesses 
any  independence  of  its  own,  but  is  simply  a  link  in  a  series,  or  a 
piece  of  a  whole  that  is  never  completed.  We  say,  therefore,  that 
causal  explanation  leads  to  an  infinite  regress.  The  notion  of  a  '  first 
cause'  is  then  contradictory,  if  'cause'  be  defined  in  the  scientific 
sense,  as  a  phenomenon  existing  in  time  and  space. 

In  the  last  section,  it  was  stated  that  causal  judgments  connect 
one  part  of  our  knowledge  with  another,  and,  in  this  way,  aid  in 
uniting  the  parts  of  our  experience  in  a  systematic  way.  Now  it  is 
undoubtedly  true  that  it  would  be  impossible  to  have  any  genuine 
knowledge  of  anything  as  a  whole,  or  an  individual,  without  know- 
ing the  way  in  which  the  parts  are  related,  and  mutually  depend 
upon. each  other.  In  that  sense,  judgments  of  causal  relation  are 
indispensable  to  a  knowledge  of  a  true  whole.  But  this  form  of 
judgment  itself  resolutely  goes  on  connecting  part  with  part  —  one 
phenomenon  with  another  —  and  refuses  to  regard  any  group  of 
parts  as  possessed  of  an  independent  character  or  individuality. 
From  this  point  of  view,  everything  is  externally  determined;  its 


372  Types  of  Judgment 

cause,  or  principle  of  explanation,  lies  outside  of  it  in  something 
else.  The  mark  of  individuality,  on  the  other  hand,  is  the  power 
of  origination,  or  self-determination.  If,  then,  there  exist  any 
genuine  individuals,  they  are  something  more  than  causally  de- 
termined phenomena. 

(2)  Psychology,  at  least  modern  structural  psychology,  adopts 
the  standpoint  of  Causal  Connection ;  while  Ethics,  assuming  that 
men  as  moral  beings  are  responsible  for  their  actions  takes  to  some 
extent  at  least  the  standpoint  of  Individuality.  The  former 
science  regards  mind  as  a  sum  of  mental  processes,  and  under- 
takes to  show  how  its  various  parts  are  connected.  Every  state 
of  consciousness  is  supposed  to  be  determined  by  something  external 
to  itself  —  some  antecedent  mental  state,  or  some  bodily  process. 
The  interest,  as  was  previously  said,  is  centered  in  the  parts,  and  it 
is  very  rarely  that  the  psychologist  stops  to  look  at  the  mind  as  a 
whole.  Ethics,  on  the  other  hand,  has  to  begin  with  the  individual. 
It  does  not  regard  mind  as  a  thing  or  substance  (that  is  the  naive 
point  of  view  against  which  psychology  rightly  warns  us),  but  as 
a  self-conscious  system  of  ideas,  purposes,  and  feelings,  which  pos- 
sesses the  power  of  initiating  action,  and  of  determining  itself  in  ac- 
cordance with  some  purpose.  The  judgment  of  Individuality, 
as  a  more  concrete  form,  must  use  the  results  of  judgments  of 
Causal  Connection.  What  it  really  does,  is  to  interpret  what  for 
the  psychologist  is  a  sum  of  mental  processes  in  terms  of  a 
system  which  has  a  real  unity  of  its  own.  For  it  is  only  when  a 
person  is  regarded  as  a  self-conscious  and  self-acting  individual, 
that  he  can  be  supposed  capable  of  conduct  to  which  the  terms 
'moral'  and  'immoral'  can  properly  be  applied. 

REFERENCES 

Hegel,  Logic,  Pt.  II.,  The  Doctrine  of  Essence  (Wallace's  trans.  2d 
ed.),  pp.  206-286. 

B.  Bosanquet,  Logic,  Vol.  I.,  Chs.  II.— V. 
J.  S.  Mill,  Logic,  Bk.  III.,  Ch.  V. 

C.  Sigwart,  Logic,  §  73. 


CHAPTER    XXV 

THE    NATURE  OF    INFERENCE.  — INDUCTION   AND    DEDUCTION 

§  91.  Judgment  and  Inference.  —It  must  not  be  forgotten 
that  our  object  in  these  chapters  is  to  obtain  as  definite  a  con- 
ception as  possible  regarding  the  nature  of  thought.  To 
attain  this  end,  we  agreed  (§  76)  that  it  would  be  advanta- 
geous to  begin  with  the  simplest  or  most  elementary  form  of 
thinking.  That  form  we  found  to  be  Judgment.  We  have 
now  endeavoured  to  show  what  Judgment  is,  and  what  part 
it  plays  in  building  up  knowledge.  And,  in  the  last  chap- 
ter, we  have  attempted  to  see  some  of  the  steps  in  the  evolu- 
tion of  Judgment,  as  it  passes  from  simple  judgments  of 
Quality  to  judgments  of  Individuality.  This  account  being 
completed,  it  remains  now  to  discuss  the  nature  of  Reasoning, 
or  Inference,  as  the  process  in  which  judgment  occurs. 

We  shall  probably  get  the  clearest  idea  of  the  nature  of 
Inference  by  regarding  it  as  a  completely  developed  judg- 
ment. As  thinking  develops  from  the  form  of  simple  judg- 
ment to  that  of  Inference,  it  displays  progressive  differen- 
tiation and  integration.  In  accordance  with  this  law,  we 
can  say,  (1)  that  Inference  is  more  complex  than  Judgment. 
The  latter  process,  in  its  simplest  form,  can  scarcely  be  said 
to  have  any  parts:  it  represents  a  single  act  or  pulsation  of 
intelligence.  Inference,  on  the  other  hand,  seems  to  imply 
steps  or  stages  in  thinking  —  a  passage  of  the  mind  from  one 

373 


374  The  Nature  of  Inference 

fact  to  another.    Moreover,  (2)  Inference  differs  from  Judg- 
ment in  exhibiting  the  grounds  upon  which  its  statement 
rests.    The  simple  judgment  makes  a  declaration  on  the  basis 
of  sense-perception,  as,  for  example,  '  the  mail-train  has  just 
gone  down  ';    'it  rained  yesterday.'     Each  of  these  state- 
ments stands  alone,  as  it  were;    it  does  not  attempt  to  gain 
support  by  pointing  out  the  connection  of  the  asserted  fact 
with  other  facts.    To  infer,  however,  is  just  to  show  the  nec- 
essary connection  of  facts  ■ —  that  from  the  presence  or  ab- 
sence of  certain  things,  the   presence  or  absence  of  certain 
other  things   necessarily   follows.     It   is  not   necessary   for 
Inference  that  the  conclusion  reached  should  be  a  fact  which 
was  not  hitherto  known.     We  often  do  reach  new  truths  by 
reasoning    from    necessary    connections.    Thus    we    might 
infer  that  the  mail-train  has  just  gone  down,  from  the  fact 
that  this  train  is  always  on  time,  and  that  it  is  now  five  min- 
utes past  the  hour.    Or,  we  might  prove,  to  a  person  who 
doubted  the  correctness  of  our  memory,  that  it  rained  yester- 
day, by  pointing  to  other  facts  with  which  rain  is  necessarily 
connected.       We  might  point    to    the  muddy  condition  of 
the  roads,  the  swollen  streams,  or,  perhaps,    might  remind 
the  person  who  questions  the  statement,  that  it   was  yester- 
day that  A  was  out  driving,  and  came  home  soaking.     In 
this  way,  one  tries  to  exhibit  the  necessity  of  the  fact  under 
consideration;   and  to  do  this  is  to  infer. 

But  in  the  actual  process  of  knowledge,  we  more  frequently 
go  from  a  fact  to  its  reasons,  than  in  the  opposite  direction. 
The  intelligence  begins  by  accepting  all  the  connections  as 
true  and  universal  which  it  meets  with  in  ordinary  expe- 
rience, or  which  are  suggested  to  it  in  any  way.  It  does  not 
trouble  itself  at  all  about  the  grounds  of  its  judgments,  and 


§  91.  Judgment  and  Inference  375 

thus  the  insufficient  basis  on  which  many  of  these  stand  is  at 
first  not  evident.  The  child,  for  example,  believes  every- 
thing which  it  is  told  by  its  mother  or  nurse,  or,  it  may  be,  all 
the  pleasant  things  which  it  imagines.  Very  often,  too,  the 
judgments  of  older  persons  are  determined  by  their  own 
wishes.  The  French  peasant  girl  was  sure  that  it  was  im- 
possible for  the  Germans  to  take  Paris.  Another  principle 
upon  which  both  children  and  adults  quite  unconsciously 
proceed,  is  that  the  future  must  always  resemble  the  past. 
The  child  assumes  that  the  order  of  events  each  day  will  be 
the  same,  —  that  there  will  always  be  games  after  dinner, 
and  visitors  in  the  afternoon,  because  that  has  happened  a 
number  of  times  in  the  past.  And  one  may  have  no  better 
reason  for  believing  that  the  sun  will  rise  to-morrow,  than 
the  fact  that  it  rose  yesterday  and  to-day. 

In  these  early,  unreflective  judgments,  the  ground  or  prin- 
ciple upon  which  they  are  based  is,  of  course,  not  conscious 
at  all.  Each  judgment  is  accepted  by  itself,  and  no  questions 
are  raised  as  to  how  it  is  known.  But  the  development  of 
intelligence  may  be  regarded  as  a  process  of  becoming  con- 
scious of  the  reasons  which  show  the  falsity  of  certain  of  our 
beliefs  and  the  necessity  of  others.  The  original  judgment 
is  not  in  reality  so  isolated  and  unrelated  as  it  appeared;  it 
contains  implicitly  its  own  reasons.  But  the  validity  of 
its  procedure  cannot  be  made  manifest,  until  the  reasons 
for  the  statement  made  by  the  judgment  are  brought  to  light. 
In  the  development  of  knowledge,  the  judgment  must  ex- 
pand so  as  to  show  the  reasons  which  it  necessarily  presup- 
poses. In  itself,  it  is  only  a  fragment  of  the  complete  state- 
ment, and  it  tries  to  complete  itself  by  making  clear  the  nature 
of  the  whole  which  it  involves,  or  to  which  it  really  belongs. 


376  The  Nature  of  Inference 

It  is  not  until  the  implicit  reasons  which  every  judgment 
contains  are  thus  brought  to  consciousness,  that  it  can  be 
either  proved  or  disproved.  Taking  the  mere  judgment 
by  itself,  it  is  only  possible  to  place  one  man's  assertion 
against  another's  denial.  But  proof  or  disproof  of  a  propo- 
sition implies  that  reasons  are  given  for  or  against  it.  If  its 
connection  with  some  fact,  or  set  of  facts,  known  to  be  true, 
becomes  evident  on  reflection,  the  felt  necessity  which  the 
judgment  possesses  (§  81)  is  transformed  into  a  logical 
necessity.  But,  if  no  such  connection  can  be  found,  or,  if 
the  judgment  in  question  is  seen  to  presuppose  propositions 
which  are  themselves  false,  we  must,  of  course,  cease  to 
regard  it  as  valid. 

When  a  judgment  develops  so  as  to  become  conscious  of 
its  reasons,  it  has  already  taken  on  the  form  of  Inference. 
And,  as  we  have  already  seen,  this  is  the  usual  procedure  of 
knowledge.  We  begin  by  believing  without  reason,  or  we 
assume  that  certain  things  are  true,  and  try  to  find  reasons 
for  our  belief.  The  conclusion,  which  is,  of  course,  logically 
last,  is  usually  first  for  us,  and  we  set  out  from  it  to  find  the 
grounds,  or  the  premises. 

This  way,  however,  of  proceeding  from  conclusion  to  prem- 
ises, or  from  a  judgment  to  its  reasons,  implies  that  the 
mind  is  already  aware  of  the  distinction  between  false  know- 
ledge and  true,  and  therefore  that  the  work  of  criticising  and 
testing  knowledge  has  already  begun.  The  criticism  of  knowl- 
edge is  probably  forced  upon  the  mind  at  first  by  the  practical 
consequences  of  false  judgments.  So  long  as  false  judgments 
lead  to  no  unpleasant  results,  they  are  likely  to  pass  unnoticed, 
without  any  question  being  raised  regarding  the  grounds 
by  means  of  which  they  are  supported.    The  child  usually 


§  91.  Judgment  and  Inference  377 

believes  all  that  he  is  told,  until  he  discovers  that  his  credu- 
lity is  making  him  a  laughing  stock,  or  has  led  to  the  loss  of 
some  pleasure  which  he  values.  Sooner  or  later  he  learns 
that  the  ground  upon  which  he  has  been  unconsciously  pro- 
ceeding —  somebody  told  me  —  is  insufficient.  In  the  same 
way,  the  natural  tendency  to  regard  all  connections  which  we 
happen  to  find  existing  between  events  as  universal  and 
necessary,  becomes  more  critical  and  discriminating.  The 
child  soon  learns  that  the  events  of  one  day  do  not  necessarily 
follow  in  the  order  of  the  day  before,  and  that  it  is  not  always 
rainy  on  Fridays,  and  fine  on  Sundays.  But,  in  order  to 
discriminate  between  what  is  true  and  what  is  false,  he  is 
obliged  to  go  beyond  the  facts  themselves,  and  to  become 
more  or  less  clearly  aware  of  the  grounds  assumed  in  each 
type  of  judgment.  He  is  forced  to  include  in  the  judgment 
the  reasons  by  which  it  is  supported.  And,  in  this  way,  the 
distinction  between  valid  and  invalid  principles  of  connection 
is  gradually  learned.  Through  experience,  which  is  more 
or  less  dearly  bought,  we  learn  that  we  cannot  depend 
upon  hearsay,  and  also  that  many  of  the  most  obvious  con- 
nections between  events  are  not  essential,  and  have  no  claim 
to  be  regarded  as  universal  laws.  It  becomes  evident  that 
it  is  necessary,  in  order  to  reach  true  principles  of  connec- 
tion, to  take  a  wider  survey  of  the  facts,  and  to  push  the 
process  of  analysis  further  than  is  done  by  our  ordinary 
judgments  of  sense-perception.  For  example,  we  may  at 
one  time  have  supposed  it  to  be  a  universal  law  that  hot 
water  will  break  glasses  when  poured  into  them.  But  as 
soon  as  we  have  experience  of  any  instance  or  instances  to 
the  contrary,  we  see  that  there  is  no  essential  connection 
between  hot  water  and  broken  glasses.     It  is  necessary  then 


378  The  Nature  of  Inference 

to  go  behind  the  obvious  facts  of  the  case,  in  order  to  disco vei 
what  is  the  real  antecedent  in  the  two  cases.  The  two  in. 
stances  —  where  the  glasses  break,  and  where  they  do  not  — 
seem  to  be  the  same ;  and  yet,  since  the  result  is  different, 
there  must  be  a  difference  which  further  analysis  will  bring 
to  light,  such  as  the  greater  thickness  of  the  glasses  which 
break.  It  is  by  penetrating  beneath  the  point  of  view  of 
ordinary  knowledge,  that  science  endeavours  to  show  how 
phenomena  are  really  and  essentially  connected. 

The  judgments  of  ordinary  adult  life  usually  involve  some  con- 
sciousness of  their  grounds,  and  are  therefore  so  far  inferences. 
But  in  many  cases  of  this  kind  it  would  be  difficult  for  the  individual 
to  state  explicitly  the  reasons  for  his  judgment.  The  connection 
which  he  asserts  may  be  guaranteed  to  his  mind  by  some  complex 
set  of  circumstances  very  difficult  to  formulate.  Or  it  may  rest 
upon  some  general  similarity  or  analogy,  which  is  so  obviously  in- 
sufficient that  he  hesitates  to  acknowledge  that  it  is  the  only  ground 
he  has  for  judging.  Thus  one  may  be  vaguely  conscious  that 
one's  only  reason  for  1  king  A  is  his  resemblance  to  B.  It  may  be 
impossible  to  say  exactly  in  what  points  A  resembles  B;  one  may 
proceed  on  a  vague  general  similarity.  Or  one  may  hesitate  to 
make  clear,  even  to  oneself,  that  the  only  reason  for  disliking  A  is 
because  of  some  external  resemblance  —  in  name,  or  dress,  or 
figure  —  to  C,  whom  one  dislikes. 

§  92.  The  Nature  of  Inference.  — We  have  seen  that  it  is 
difficult  to  draw  any  hard  and  fast  line  between  Judgment 
and  Inference.  In  general,  however,  we  may  be  said  to 
reason  when  we  do  not  simply  accept  a  fact  on  the  basis  of 
sense-perception  or  memory,  but  show  that  it  necessarily 
follows  from  some  other  known  fact  or  facts.  Inference, 
then,  requires  (1)   that  certain  data  or  premises  should  be 


§  92.    The  Nature  of  Inference  379 

accepted  as  already  known;  and  (2)  it  implies  an  insight 
into  the  necessary  connection  of  some  new  fact  or  set  of  facts 
with  what  we  already  know.  Thus  one  is  said  to  infer  B 
when  one  sees  that  it  necessarily  follows  from  some  fact 
which  is  already  known.  It  is  not  necessary  for  an  inference 
that  B  should  never  have  been  in  consciousness  before.  As 
we  have  seen  in  the  last  section,  what  we  very  often  do  in 
inference  is  to  show  the  reasons  or  necessity  of  some  fact 
which  we  have  previously  accepted  without  knowing  why. 
No  matter  whether  we  go  from  premises  to  conclusion  (from 
the  reasons  to  the  fact),  or  in  the  opposite  direction,  from  the 
conclusion  to  the  premises,  we  are  said  to  infer  whenever 
we  find  the  ground  for  the  existence  of  one  fact  in  the  nature 
of  another  fact.  In  the  former  case,  we  use  words  like  '  there- 
fore '  and  '  consequently,'  to  indicate  the  connection;  or, 
when  the  reasons  are  stated  last,  we  use  '  for  '  and  '  because.' 
Whenever  these  conjunctions  are  used  correctly,  an  inference 
has  been  made,  and  it  is  always  useful  in  following  a  course 
of  reasoning  to  make  clear  to  ourselves  precisely  on  what 
grounds  it  has  been  made. 

Although  Inference  seems  very  simple  and  very  natural, 
its  procedure  is  much  more  puzzling,  when  looked  at  closely, 
than  one  would  at  first  imagine.  As  we  have  seen,  there  is 
no  Inference  unless  the  result  reached  is  different  from  the 
starting-point.  But  how  are  we  ever  justified  in  passing  from 
a  knowledge  of  one  fact  to  another  different  from  it  ?  How 
can  we  ever  pass  from  the  known  to  the  unknown  ?  The 
Greeks,  who  loved  to  bring  to  light  the  paradoxes  which  so 
often  underlie  familiar  facts,  used  to  discuss  this  question. 
How  is  it  possible  for  that  which  is  unknown  —  external  to 
*he  mind  — to  pass  into  the  mind  and  get  itself  known?    It 


380  The  Nature  of  Inference 

was  to  solve  this  puzzle  that  Plato  propounded  the  doctrine 
that  all  knowing  is  remembering.1  Knowledge,  he  declared, 
is  not  increased  by  learning  that  of  which  we  were  altogether 
ignorant,  but  by  a  process  of  calling  to  mind  or  recollecting 
the  knowledge  which  the  soul  possessed  in  a  previous  state 
of  existence,  but  which  was  forgotten  when  it  entered  upon 
the  conditions  of  the  present  life.  It  was  therefore  not  neces- 
sary to  suppose,  according  to  Plato,  that  the  mind  performed 
the  impossible  feat  of  knowing  what  is  external  to  itself,  or 
that  things  previously  unknown  pass  bodily  into  our  minds, 
and  thus  become  known. 

Plato  was  undoubtedly  right  in  protesting  against  the 
popular  view  that  knowledge  is  received  into  the  mind  in 
mechanical  fashion,  as  food  is  received  into  the  stomach. 
Knowledge,  as  we  have  frequently  seen,  is  built  up  from 
within,  and  not  put  in  from  without.  But  the  apparent  para- 
dox of  knowledge  may  be  explained  without  adopting  Plato's 
poetical  notion  of  a  previous  state  of  existence.  We  may 
admit  that  the  process  of  inference  would  be  quite  inexpli- 
cable, if  it  preceded  from  one  fact,  A,  to  a  knowledge  of  a  sec- 
ond fact,  B,  which  is  totally  different  from  the  former.  When 
we  examine  cases  of  inference,  however,  we  find  that  there  is 
always  a  certain  amount  of  identity  between  the  two  ends  of 
the  process.  The  conclusion  is  always  different,  and  yet  not 
entirely  different  from  the  premises.  Thus,  from  the  propo- 
sitions, '  all  metals  are  elementary  substances,'  and  '  gold  is 
a  metal,'  one  can  infer  that  gold  is  an  elementary  substance. 
It  is  possible  to  connect  '  gold  '  and  '  elementary.'  Here  the 
identical  link  —  what  is  called  in  formal  logic  the  middle 

1  This  is  the  theory  upon  which  Wordsworth  based  his  "  Ode  on  the 
Intimations  of  Immortality." 


§  92.    The  Nature  of  Inference  381 

term — is  'metal.'  It  is  possible  to  connect  gold  and  ele- 
mentary substance,  because  the  former  is  at  the  same  time  a 
metal,  which  in  its  turn  is  an  element.  Of  course,  these  con- 
ceptions—  gold,  metal,  element — are  not  absolutely  iden- 
tical ;  it  was  pointed  out  in  §  84  that  propositions  cannot 
be  regarded  as  expressing  mere  identity  without  difference. 
But  we  can  say  that  there  is  a  common  thread  or  element 
running  through  these  notions,  which  furnishes  the  principle 
of  connection.  Where  we  cannot  discover  such  a  common 
nature,  no  inference  can  be  made.  Thus,  for  example,  it 
would  be  impossible  to  draw  any  conclusion  from  the  state- 
ments that  '  it  rained  yesterday  '  and  '  gold  has  been  dis- 
covered in  Alaska,'  because  there  is  no  common  element  or 
connecting  thread  present  which  would  lead  us  beyond  the 
premises. 

In  formal  arguments  the  middle  term,  or  connecting  link, 
is  usually  explicitly  stated;  but  in  the  actual  process  of  rea- 
soning things  out,  it  is  frequently  necessary  to  go  in  search 
of  it.  We  may  notice,  for  example,  that  the  fire  in  a  stove 
burns  more  slowly  when  the  damper  is  shut.  In  order  to 
understand  the  fact,  we  have  to  find  out  some  fact  which  is 
common  to  '  closed-damper '  and  '  slow-burning,'  some  link 
of  identity,  as  it  were,  which  enables  us  to  pass  from  the  one 
to  the  other.  Such  a  connecting  link  is  afforded,  of  course,  in 
this  case  by  the  supply  of  oxygen.  Darwin  was  noted  for  his 
keenness  in  detecting  connections  which  escape  the  ordinary 
eye,  as  well  as  for  his  skill  in  giving  explanations  of  them. 
On  one  occasion,  he  observed  that  in  the  part  of  the  country 
where  he  lived,  clover  was  abundant  in  those  fields  which 
were  situated  near  villages,  while  the  outlying  fields  were 
almost  destitute  of  it.     What  now,  he  asked  himself,  is  the 


382  The  Nature  of  Inference 

connecting  link  between  these  facts?  Some  investigation 
of  the  matter  convinced  him  that  the  three  agencies  which 
produced  this  result  were  humble-bees,  mice,  and  cats.  The 
bees  fertilize  the  clover  flowers,  and  thus  male  the  plant 
abundant,  the  field  mice  destroy  the  bees'  nests,  but  the  cats 
go  out  from  the  villages  into  the  fields  near  by  and  kill  the 
mice. 

We  have  seen  that  the  passage  from  one  fact  to  another  in 
inference  does  not  involve  a  transition  to  something  wholly 
different  from  the  starting-point.  There  is  always  some 
aspect  or  feature  in  which  the  premises  are  identical  with 
the  conclusion.  And  it  is  on  the  strength  of  this  identity 
that  a  passage  can  be  made  from  one  to  the  other.  The  same 
fact  may  be  expressed  differently  by  saying  that  all  inference 
takes  place  within  a  system,  '  where  the  parts  are  so  held 
together  by  a  common  nature  that  you  can  judge  from 
some  of  them  what  the  nature  of  the  others  must  be.'  Sup- 
pose you  were  given  the  leaf  of  a  plant.  If  you  had  some 
systematic  botanical  knowledge,  it  might  be  possible  to  infer 
the  species  of  plant  to  which  the  leaf  belonged.  That  is, 
from  the  nature  of  a  part,  the  nature  of  the  whole  to  which 
it  belongs  could  be  determined.  The  part  represents  the 
whole  —  in  some  sense  contains  it  implicitly.  It  is  said 
that  the  great  naturalist  Cuvier  could  determine  by  exam- 
ining a  single  tooth  the  nature  of  the  animal  to  which  it 
belonged.  Let  us  suppose  that  the  tooth  were  that  of  a 
ruminant  animal.  Now  a  zoologist,  who  knows  the  character- 
istics of  such  an  animal,  could  draw  various  inferences  regard- 
ing the  possessor  of  the  tooth.  He  could  conclude,  for 
example,  that  the  animal  to  which  it  once  belonged  must  also 
have  had  cloven  hoofs.     A  single  piece  or  part,  that  is,  would 


§  92.    The  Nature  of  Inference  383 

enable  one  who  knows  accurately  the  system  or  common 
nature  to  which  all  the  parts  belong,  to  judge  what  the  other 
parts  are  like. 

The  examples  just  given  have  referred  to  the  possibility 
of  an  inference  from  one  part  of  an  organism  to  another.  But; 
as  we  have  already  seen,  the  systematic  connection  which 
here  exists  between  the  parts  is  more  or  less  completely 
present  whenever  it  is  possible  to  infer  at  all.  Inference 
pushes  further  the  work  of  constructing  a  system  begun  by 
Judgment  (§  83).  If  each  thing  were  known  by  itself,  if  the 
parts  of  our  knowledge  did  not  fall  together  into  systems 
where  each  part  to  some  extent  determines  the  nature  of  the 
other  parts,  no  inference  would  be  possible.  It  is  because 
the  various  pieces  of  our  knowledge  are  never  independent  of 
one  another,  but  form  an  organic  whole,  like  the  members  of 
a  living  organism,  that  certain  facts  follow,  as  we  say,  from 
certain  other  facts.  Otherwise  we  could  only  guess,  or  infer 
vaguely  on  the  expectation  that  the  future  will  resemble  the 
past.  Even  this  expectation,  however,  has  no  rational 
basis,  unless  the  world  does  form  some  kind  of  a  coherent 
system.  It  is,  of  course,  true  that  practically  a  great  deal 
of  the  knowledge  of  every  one  is  unsystematic,  being  com- 
posed of  facts  and  theories  which  have  never  been  brought 
into  relation.  But  knowledge  is  not  to  be  described  in  terms 
of  such  defects  in  the  case  of  individuals.  To  understand  it, 
we  must  take  it  at  its  best  and  in  its  most  complete  form.  It 
is  obvious  that,  as  our  knowledge  in  any  field  becomes  more 
completely  and  exactly  organized,  it  it  will  be  increasingly  pos- 
sible to  use  it  as  a  basis  for  inference.  The  better  we  are  able 
to  put  together  in  a  systematic  way  the  various  facts  which 
we  have  learned  about  geology,  or  astronomy,  or  the  weather 


384  The  Nature  of  Inference 

the  more  significant  each  fact  becomes.  The  geologist  may 
be  able  to  tell  from  the  appearance  of  the  cliffs  what  has 
taken  place  in  a  locality  thousands  of  years  ago.  And, 
similarly,  for  the  fisherman,  the  temperature,  direction  of 
the  wind,  its  rising  or  falling,  etc.,  are  all  signs  from  which  he 
is  able  to  infer,  more  or  less  correctly,  the  kind  of  weather 
which  may  be  expected.  A  person  who  had  no  systematic 
knowledge  in  either  of  these  fields  would,  however,  see  noth- 
ing in  the  scarred  rocks,  or  in  the  sudden  changes  of  the  wind; 
he  might  notice  the  facts,  but  would  not  be  able  to  use  them 
as  a  basis  of  inference. 

It  is  important  to  notice  that  what  has  just  been  said  goes 
to  confirm  our  previous  statements  regarding  the  increasing 
degree  of  integration  which  knowledge  shows  in  the  course 
of  its  development.  The  knowledge  of  the  scientist  differs 
from  that  of  the  ordinary  man,  not  only  in  the  greater  number 
of  facts  which  the  former  contains,  but  also,  as  we  have  seen, 
in  the  degree  of  integration  or  coherence  which  these  facts 
possess.  Inference,  then,  is  simply  a  deep  insight,  based  on 
definite  knowledge,  into  the  necessary  connection  of  things. 
It  is  an  act  of  thought  which  discovers  the  essential  relations 
between  things  which  at  first  sight  appear  to  have  no  con- 
nection with  one  another.  As  has  already  been  said,  it  is  a 
reasoned  judgment;  i.e.  a  judgment  which  has  become  con- 
scious of  the  reasons  for  the  connections  which  it  affirms. 

§93.  Induction  and  Deduction. —It  has  been  already 
pointed  out  that  there  are  two  directions  in  which  inference 
or  reasoning  may  proceed.  We  may  begin  with  certain 
facts  or  principles  which  are  already  known,  or  are  assumed 
to  be  true,  and  proceed  to  show  that  some  result  necessarily 
follows  from  them.    Thus  we  might  infer,  from  our  know- 


§  93-    In  due  ti  oft  and  Deduction  385 

ledge  of  chemical  principles,  that  if  the  draughts  of  a  stove  are 
closed  so  that  the  supply  of  oxygen  is  lessened,  the  fire  will 
burn  slowly;  or  from  the  relative  positions  and  revolutions 
of  the  planets,  astronomical  reasoning  might  lead  to  the  con- 
clusion that  an  eclipse  of  the  sun  will  take  place  on  a  specified 
day  and  hour.  This  method  of  reasoning  is  known  as  De- 
duction. It  proceeds,  as  we  have  seen,  from  premises  to 
conclusion.  In  the  first  part  of  this  book,  this  form  of  reason- 
ing has  been  treated  at  some  length  and  its  rules  of  procedure 
stated.  At  present,  we  need  only  notice  that  in  deductive 
reasoning,  the  particular  case  is  always  brought  under  some 
general  law  or  principle,  which  is  already  known  or  assumed 
as  true.  Socrates  is  known  to  be  mortal,  because  as  a  man  he 
falls  under  the  general  law  that  all  men  are  mortal ;  the  clos- 
ing of  the  draughts  is  a  case  of  lessened  supply  of  oxygen, 
and,  therefore,  in  accordance  with  the  general  law,  a  case  of 
slow  burning.  A  deductive  inference  shows  what  are  the 
results  of  the  application  of  a  general  law  to  particular  facts 
or  instances.  It  proceeds  downwards,  as  it  were,  from  the 
general  law  to  its  consequences. 

In  Induction,  on  the  contrary,  the  procedure  is  just  the 
opposite  of  this.  We  begin  with  particular  phenomena,  and 
try  to  discover  from  them  the  law  or  principle  which  unites 
them.  Certain  facts  are  observed  to  happen  together,  and 
the  problem  is  to  find  the  ground  or  explanation  of  this  con- 
nection. Inductive  inference  is  thus  a  process  of  reading 
the  general  law  out  of  the  particular  facts,  of  transforming 
the  hypothetical  answer  to  the  problem  into  a  systematic  prin- 
ciple or  theory.  It  is  an  insight  into  the  nature  of  the  whole 
or  system,  based  upon  a  careful  examination  of  the  parts. 
'  Yesterday  the  smoke  tended  to  fall  to  the  ground,  and  it 

2C 


386  The  Nature  of  Inference 

rained  in  the  afternoon.'  These  two  facts  may  simply  be 
observed  a  number  of  times  without  any  thought  of  their 
connection.  But  intelligence  asks:  Why  should  they  happen 
in  conjunction  ?  And  to  answer  this  question,  we  must 
begin  by  analyzing  the  facts  in  our  possession.  When  the 
smoke  falls  to  the  ground,  the  atmosphere  must  be  lighter 
than  usual ;  this  is  the  case  when  it  contains  a  great  deal  of 
moisture;  but  when  the  atmosphere  is  in  this  condition,  it 
usually  tends  to  discharge  its  moisture  in  the  form  of  rain: 
therefore  we  have  the  general  law  which  enables  us  to  show 
that  the  behaviour  of  the  smoke  and  the  rain  yesterday  were 
not  only  accidentally  conjoined,  but  essentially  connected. 

Deduction  and  Induction,  then,  are  both  forms  of  infer- 
ence, but  the  starting-point  and  mode  of  procedure  of  the 
one  is  different  from  that  of  the  other.  Consequently,  it  is 
not  unusual  to  speak  of  them  as  two  kinds  of  reasoning  which 
are  quite  distinct  and  independent  of  each  other.  It  is,  how- 
ever, important  to  avoid  this  popular  error,  and  to  remember 
that  the  real  process  of  inference  is  in  each  case  the  same. 
The  essence  of  inference,  as  has  been  shown,  consists  in  the 
fact  that  it  exhibits  the  manner  in  which  particular  facts  are 
connected  together  into  a  system  or  whole.  And  this  end  is 
achieved  by  both  Deduction  and  Induction.  In  the  former 
case,  the  general  law  of  connection  —  what  we  may  call  the 
nature  of  the  system  within  which  the  particulars  fall  —  is 
known,  and  we  argue  from  this  as  to  the  nature  and  relations 
of  the  various  parts  which  fall  within  it.  We  have  the  com- 
mon thread  which  unites  the  various  facts  in  our  hand,  and 
following  it  out  are  able  to  show  its  application  in  determining 
the  nature  of  events  which  have  not  yet  come  within  the  range 
of  our  experience.     Knowing  the  law  of  gravity,  for  example, 


§  93-    Induction  and  Deduction  387 

one  could  infer  deductively  what  momentum  a  ball  weighing 
one  pound  must  necessarily  have  after  falling  one  hundred 
feet.  It  would  not  be  necessary  actually  to  measure  the  mo- 
mentum of  the  falling  body  in  this  particular  case,  but  it 
could  be  shown  to  be  the  necessary  result  of  the  general  law. 
What  the  deductive  inference  shows  us  is  the  way  in  which 
a  general  principle  or  law  of  connection  runs  through  a  group 
of  facts,  and  constitutes  them  a  real  or  organic  whole.  The 
same  insight  is  reached  by  inductive  inference,  although  the 
starting-point  is  entirely  different.  As  we  have  already 
seen,  induction  begins  by  observing  that  certain  phenomena 
are  frequently  conjoined,  and  attempts  to  discover  some  law 
or  principle  which  will  make  the  fact  of  their  connection 
intelligible. 

It  is  usual  to  say  that  in  induction  we  go  from  the  par- 
ticular facts  to  the  general  law.  The  following,  however, 
would  be  a  more  correct  form  of  statement:  Before  the 
inference,  we  observe  that  a  number  of  phenomena  occur 
together,  but  do  not  know  whether  this  conjunction  is  nec- 
essary or  not ;  or,  if  we  assume  that  it  is  necessary,  we  do 
not  understand  why  it  should  be  so.  As  a  result  of  the  induc- 
tive inference,  we  gain  an  insight  into  the  necessary  connec- 
tion of  the  observed  phenomena,  and  also  understand  the 
principle  according  to  which  the  latter  are  united.  What 
we  really  obtain  through  an  inductive  inference  is  not  only  a 
general  law,  but  also  a  perception  of  its  concrete  application 
to  particular  phenomena.  This  being  so,  it  is  clear  that 
Induction  and  Deduction  are  not  two  different  kinds  of 
inference.  Inference  always  implies  an  effort  on  the  part 
of  the  mind  to  see  how  phenomena  are  necessarily  connected 
according  to  some  general  principle.     And,  in  carrying  out 


388  The  Nature  of  Inference 

this  purpose,  the  mind  must  begin  with  the  knowledge  which 
it  already  possesses.  When  the  general  law  of  connection 
is  known,  and  the  object  is  to  discover  the  nature  of  some 
particular  fact,  the  method  of  procedure  is  deductive.  But, 
when  the  problem  by  which  we  are  confronted  is  to  read  out 
of  the  facts  of  sense-perception  the  general  law  of  their 
connection,  the  method  of  inference  which  must  be  employed 
is  that  of  Induction.  But,  from  whatever  point  we  set  out, 
and  whatever  may  be  the  immediate  object  of  the  inference, 
the  result  is  always  the  same  —an  insight  into  the  necessary 
connection  of  facts  according  to  some  general  principle. 

It  is  not  unusual  to  hear  the  remark  made  that  modern 
science  has  been  built  up  by  the  employment  of  the  inductive 
method.  This  must  not,  however,  be  interpreted  to  mean 
that  deductive  inferences  are  not  also  used  in  the  discovery 
of  scientific  truth.  Science  (which  is  simply  another  name  for 
systematic  knowledge)  is  the  product  of  thinking;  and  thought, 
as  we  have  seen,  is  not  limited  to  any  one  mode  of  procedure. 
Thought  aims  at  extending  knowledge,  and  so  long  as  it  can 
find  any  link  of  connection,  or  guiding  thread,  it  is  not  limited 
to  any  one  direction,  or  to  any  fixed  mode  of  working.  It  is, 
of  course,  to  be  admitted  —  and  this  is  the  truth  in  the  state- 
ment which  we  have  quoted  —  that  general  laws  cannot  be 
discovered  without  an  examination  of  particular  facts,  and 
that  their  validity  must  always  be  tested  by  comparison  with 
the  facts.  But  as  soon  as  a  general  law  is  discovered  in  any 
field,  it  is  always  used  as  a  principle  from  which  to  deduce 
new  results.  When  it  is  possible  to  employ  mathematics  in 
the  calculation  of  these  results,  it  is  usually  possible  to  extend 
our  knowledge  of  the  subject  much  more  rapidly  than  before. 
Thus  physics  and  astronomy  owe  their  rapid  development  to 


§  93-    Induction  and  Deduction  389 

the  application  of  mathematics.  It  must  be  remembered, 
however,  that  this  presupposes  a  certain  stage  of  advance- 
ment —  a  certain  inductive  stage,  as  it  were  — on  the  part  of 
the  science.  But  even  in  this  earlier  stage  we  are  constantly 
employing  deduction,  always  reasoning  out  the  results  of  cer- 
tain guesses  or  suggestions  to  see  if  they  hold  true  (cf.  §  48). 
Both  in  ordinary  life  and  in  scientific  procedure  Induction 
and  Deduction  are  constantly  employed  together  as  mutually 
supplementing  each  other  in  the  work  of  organizing  expe- 
rience. 

REFERENCES 

B.  Bosanquet,  Logic,  Vol.  II.,  Ch.  I. 

F.  H.  Bradley,  The  Principles  of  Logic,  pp.  430-468. 

W.  James,  The  Principles  of  Psychology,  Vol.  II.,  Ch.  XXII. 

J.  G.  Hibben,  Inductive  Logic,  Chs.  I.  and  II. 


CHAPTER   XXVI 

THE   UNIFICATION    OF   KNOWLEDGE 

§  94.  Science  and  Philosophy.  —  Throughout  the  pre- 
ceding chapters  thinking  has  been  described  as  the  function 
through  which  the  organization  of  experience  is  achieved, 
or  as  a  process  of  building  up  a  system  of  knowledge.  It 
has  become  clear  that  the  development  of  thinking  involves 
a  continuous  increase  in  both  differentiation  and  integration, 
and  that  these  two  moments  or  aspects  of  thought  are  or- 
ganically related  to  each  other.  An  advance  in  knowledge 
implies  at  once  new  facts  and  distinctions,  and  also  the  per- 
ception of  new  connections  and  relations  among  facts.  The 
ideal  of  completed  knowledge,  accordingly,  would  be  a 
system  of  truths  in  which  the  place  and  meaning  of  every 
fact  would  be  completely  denned,  and  where,  at  the  same 
time,  the  complete  relation  of  every  fact  and  every  group  of 
facts  to  every  other  would  be  fully  exhibited.  Nothing 
would  then  be  indefinite  for  knowledge,  and  nothing  would 
be  isolated;  to  know  things  in  this  completely  systematic 
way  would  be  to  see  the  world  steadily  and  to  see  it  whole. 

Like  all  ideals,  this  conception  is  never  completely  realized 
in  experience  as  we  know  it.  This,  however,  does  not 
render  it  idle  or  without  practical  significance.  In  the  first 
place,  it  has  importance  as  indicating  the  direction  in  which 
the  further  development  of  knowledge  must  proceed.  And, 
secondly,  it  is  only  by  reading  our  actual  knowledge  in  the 

390 


§  94-    Science  and  Philosophy  391 

light  of  the  end  towards  which  it  is  progressing  that  we  are 
able  to  understand  its  nature.  That  is,  as  stated  in  the 
first  section  of  this  book,  thinking  has  to  be  defined  as  the 
function,  or  system  of  functions,  whose  end  and  goal  is  know- 
ledge. Now  knowledge  is  only  attained  in  so  far  as  unifica- 
tion and  system  are  attained:  the  essence  of  knowledge  is 
not  found  in  its  lack  of  system  and  definiteness  —  these 
are  its  defects  and  privations  —  but  the  cognitive  experience 
of  any  individual  has  a  right  to  the  title  of  knowledge 
just  in  so  far  as  these  conditions  are  realized. 

The  problem  of  how  a  more  complete  unity  of  knowledge 
than  that  realized  in  the  results  of  the  special  sciences  is  to 
be  attained,  thus  becomes  of  the  highest  importance.  We 
may  use  the  term  Science  to  denote  the  entire  work  of  dis- 
covery and  systematization  of  facts  which  is  carried  on  by 
the  various  civilized  nations  through  successive  generations 
and  centuries.  In  this  inclusive  sense,  Science  is  undoubt- 
edly one  of  the  greatest  achievements  of  the  human  race, 
and  one  of  the  highest  objects  of  endeavour  for  the  individual. 
Within  this  one  body  of  knowledge,  however,  it  is  possible 
to  make  various  distinctions  between  different  sciences  and 
groups  of  sciences.  The  various  sciences  might  be  clas- 
sified, for  example,  as  more  or  less  abstract,  or  as  more  or 
less  inclusive  in  character.  Or  again,  the  sciences  of  nature 
might  be  distinguished  from  the  humanistic  sciences,  which 
deal  with  the  distinctive  products  of  man's  life  and  thought, 
as  shown,  for  example,  in  religious,  social,  or  political 
institutions,  or  in  art,  science,  and  philosophy.  But  the 
division  of  the  complete  body  of  knowledge  (Science, 
Wissenschaft)  with  which  we  are  here  directly  concerned, 
is  that  between  the  sciences  and  philosophy.     For  philos- 


392  The  Unification  of  Knowledge 

ophy  is  the  name  given  to  the  endeavour  to  reach  somfe 
rational  unification  of  the  knowledge  derived  from  the 
various  forms  of  experience,  and  especially  from  the  various 
sciences.  "Knowledge  of  the  lowest  kind,"  said  Herbert 
Spencer,  "is  un-unified  knowledge;  science  is  partially- 
unified  knowledge;  philosophy  is  completely-unified  know- 
ledge."1 We  may  accept  this  statement  with  the  under- 
standing that  of  course  no  knowledge  is  entirely  un-unified, 
and  that,  on  the  other  hand,  no  actually  existing  system  of 
philosophy  can  claim  to  have  achieved  a  complete  and  satis- 
factory unification  of  knowledge. 

At  the  present  time  the  systematic  interpretation  of  the 
nature  of  the  real  world  has  been  divided  into  various  fields  of 
investigation.      Each  science  takes  as  its  subject-matter  a 
definite  field,  or  group,  of  phenomena  and  endeavours  to 
describe  and  explain,  as  accurately  as  possible,  the  facts  that 
fall  within  that  field.     Thus,  for  example,  astronomy  studies 
the  heavenly  bodies  with  the  purpose  of  making  clear  and 
comprehensible  their  changing  phases  and  relations ;  botany 
deals  with  the  various  forms  and  functions  of  plant  life; 
history  describes  the  significant  events  which  have  occurred 
during  the  past  life  of  man  in  society.     It  is,  however,  not 
true  that  the  sciences  can  be  distinguished  merely  with  refer- 
ence to  the  nature  of  the  particular  field  which  they  occupy. 
The  same  body  of  facts  may  be  dealt  with  by  a  number  of 
sciences ;  or,  rather,  there  are  certain  more  general  or  funda- 
mental sciences  whose  principles   and  results  have  to  be 
employed  in  the  work  of  the  more  special  fields  of  inquiry. 
In  botany,  for  example,  physical  and  chemical    facts  and 
laws  are  cited  in  order  to  render  the  behaviour  of  the  plant 

1  First  Principles,  §  37. 


§  94-    Science  and  Philosophy  393 

intelligible.  In  political  economy,  in  like  manner,  one  has 
to  make  constant  use  of  history  in  the  investigations  which 
one  undertakes.  Nevertheless,  even  where  two  or  more 
sciences  seem  to  occupy  the  same  field,  it  will  be  found  that 
each  has  its  own  special  way  of  reading  the  facts,  so  that 
strictly  speaking,  the  same  phenomena  are  never  studied  in 
the  same  way  or  with  the  same  purpose  in  view. 

The  question  to  be  considered  here,  however,  is  the  ques- 
tion of  the  relation  of  the  special  sciences  to  philosophy. 
It  might  appear  at  first  sight  as  if  the  whole  field  of  reality 
were  occupied — or  soon  to  be  occupied  —  by  the  various 
sciences  and  that  no  problem  were  therefore  left  for  phi- 
losophy. But  the  very  fact  that  each  science  is  obliged,  in 
order  to  render  its  investigations  definite  and  fruitful,  to 
limit  the  field  of  its  inquiry,  makes  necessary  some  attempt 
to  bring  the  results  derived  from  the  different  fields  into 
relation.  And,  as  will  appear  more  clearly  in  the  last  section 
of  this  chapter,  to  correlate  the  results  of  these  different 
scientific  inquiries,  which  are  gathered  with  various  purposes, 
and  often  by  the  employment  of  quite  different  hypotheses, 
is  not  merely  to  set  them  side  by  side.  The  work  that  phi- 
losophy is  called  upon  to  undertake  is  to  interpret  these 
results  in  such  a  way  as  to  render  them  coherent  and  think- 
able. Philosophy  aims  at  unifying  knowledge  by  finding  a 
conception  or  set  of  conceptions  which  will  enable  us  to 
think  the  world  as  some  kind  of  a  consistent  system.  It 
seeks  to  satisfy  our  demand  for  a  world-view,  a  Weltan- 
schauung. When  we  take  the  widest  and  most  accurate 
survey  within  our  power  of  the  facts  of  experience,  what 
conclusions  are  we  warranted  in  drawing  regarding  the 
whole  system  of  things  of  which  we  are  a  part  ? 


394  The  Unification  of  Knoivledgc 

In  attempting  to  find  an  answer  to  this  most  practical 
question,  it  is  of  course  necessary  to  take  account  of  every 
well-authenticated  form  of  experience,  and  to  give  to  each 
its  proper  place  and  value.  It  is  obvious,  too,  that  the  prob- 
lem is  the  final  problem  of  knowledge,  and  one  that  cannot  be 
finally  and  fully  solved  by  any  individual  or  by  any  generation. 
But  that  is  not  a  reason  for  abandoning  it  as  insoluble.  In 
the  first  place,  it  is  a  problem  to  which  human  reason  from 
its  very  nature  can  never  be  permanently  indifferent.  It 
is  only  the  animals,  Hegel  remarks,  who  are  not  metaphy- 
sicians. It  is  true  that  the  majority  of  men  never  apply 
themselves  directly  to  the  solution  of  ultimate  philosophical 
questions;  but  every  one  holds,  more  or  less  consciously, 
and  in  more  or  less  definite  form,  some  conception  regarding 
the  nature  of  the  world  and  his  own  place  in  it.  It  is  per- 
haps most  frequently  from  theology  or  from  literature  that 
men  derive  their  world-view,  and  they  hold  this,  not  as  a 
reasoned  system  of  knowledge,  but  rather  through  belief 
in  authority,  or  on  emotional  or  aesthetic  grounds.  As 
distinguished  from  constructions  of  this  character,  philosophy 
aims  at  a  reasoned  system.  Like  the  sciences,  it  discards 
both  emotion  and  tradition  as  guides,  and  proceeding  by 
means  of  careful  analysis  and  definition,  it  subjects  all 
hypotheses  to  rational  criticism.  Its  postulate  is  that  there 
is  nothing  irrational,  or  from  its  very  nature  incomprehen- 
sible, in  the  nature  of  the  world.  It  is  true  that  science 
and  philosophy  will  never  complete  the  work  they  are  carry- 
ing on :  the  results  arrived  at  are  never  final,  but  only  start- 
ing-points for  new  investigations.  But  in  the  one  case  as  in 
the  other,  the  road  is  never  barred;  progress  is  always  pos- 
sible if  the  problem  is  formulated  in  an  intelligible  way. 


§  95-    Science  as  Philosophy  39$ 

Two  considerations,  which  are  frequently  overlooked,  fol- 
low from  the  conception  of  philosophy  as  a  construction  that 
is  being  continuously  achieved  by  the  human  race  in  the 
course  of  its  history.  The  first  is,  that  it  would  be  idle  for 
any  individual  to  begin  the  work  anew  on  his  own  account, 
refusing  to  learn  or  to  profit  by  the  labours  of  the  past.  And 
secondly,  it  is  obvious  that  from  the  nature  of  the  case 
there  will  be,  as  long  as  the  human  race  endures,  no  ultimate 
or  finally  complete  system  of  philosophy.  When  it  is  remem- 
bered that  philosophy  is  the  completion  of  the  sciences, 
that  the  philosophical  problem  is  the  final  problem  of  know- 
ledge, the  fact  that  neither  the  foundations  nor  its  outlines 
are  yet  finally  determined  will  not  appear  either  strange  or 
discouraging. 

§  95.  Science  as  Philosophy.  —  In  this  connection,  the 
question  arises  whether  the  conceptions  employed  by  the 
sciences  are  not  themselves  capable  of  effecting  a  final 
unification  of  knowledge.  Why  is  it  necessary  to  turn  to 
philosophy,  or  if  the  name  of  philosophy  is  still  used  to  denote 
the  most  comprehensive  science,  why  should  not  the  ulti- 
mate account  of  reality  be  given  in  the  same  terms  as 
the  descriptions  of  the  special  sciences  ?  Why,  in  short, 
not  accept  as  philosophy  the  general  standpoint  and  results 
of  the  sciences  ? 

As  a  matter  of  fact,  this  is  often  done.  During  the  last 
two  centuries  —  and  more  particularly  during  the  last  cen- 
tury —  the  greatest  advances  in  knowledge  have  been 
attained  in  the  field  of  the  natural  sciences.  As  a  conse- 
quence, it  has  been  natural  to  assume  that  the  same  suc- 
cess may  be  attained  everywhere  by  employing  the  same 
unifying  conceptions  in  the  solution  of  all  kinds  of  problems. 


396  The  Unification  of  Knowledge 

Now  the  fundamental  categories  with  which  natural  science 
operates  are  those  of  Quantity  and  Causality.  The  lattei 
conception,  when  used  exactly  or  scientifically,  includes  the 
former,  as  has  appeared  in  our  study  of  Induction  (cf. 
pp.  255  ff.).  The  assumption  on  which  the  causal  category 
proceeds  is  that  reality  is  composed  of  phenomena  which  are 
external  to  one  another  and  at  the  same  time  dependent  on 
one  another.  Every  phenomenon  is  at  once  a  cause  and  an 
effect.  There  obtains  everywhere  unvarying  laws  of  connec- 
tion between  all  events  so  that  nothing  can  be  thought  of  as 
happening  except  in  one  determinate  and  fixed  way.  For 
every  phenomenon  a  cause  must  be  sought  in  some  other 
phenomenon,  or  group  of  phenomena,  and  thus  everything 
is  determined  or  conditioned,  both  as  to  its  existence  and 
nature,  by  something  external  to  itself.  External  determina- 
tion, or  conditioning  through  something  external  to  that 
which  is  to  be  explained,  is  thus  the  form  of  relation  employed 
by  natural  science  in  its  work  of  unifying  knowledge. 

Now  in  attempting  to  interpret  the  entire  world  as  a 
series  of  phenomena  which  are  everywhere  related  in  terms 
of  cause  and  effect,  one  might  be  either  more  or  less  thorough- 
going and  consistent.  On  the  one  hand,  one  might  assume 
that  the  complete  unification  of  knowledge  demands  that 
there  shall  be  only  a  single  series  of  causes  and  effects.  This 
would  imply  that  all  the  phenomena  of  which  the  world  is 
composed  are  at  bottom  reducible  to  the  same  terms,  and 
are  all  manifestations  of  some  one  material,  or  one  prin- 
ciple. Or,  on  the  other  hand,  it  might  be  assumed  that  there 
is  more  than  one  series  and  more  than  one  fundamental 
principle  involved  in  the  nature  of  things.  The  first  view 
would  be  Monistic  and  the  second  Pluralistic.     I  have  said 


§  95-    Science  as  Philosophy  397 

that  the  first  is  more  thorough-going,  because  Pluralism  still 
has  to  face  the  problem  as  to  the  relation  of  the  different 
forms  of  existence  which  it  assumes.  What  is  it  that  unites 
the  pluial  forms  of  existence  into  a  single  world,  a 
universe  ? 

Without  entering  into  the  arguments  in  support  of  either 
Monism  or  Pluralism,  however,  we  may  illustrate  the  appli- 
cation of  the  causal  point  of  view  when  employed  under  either 
assumption.  Let  us  first  assume  that  everything  in  the 
universe,  without  exception,  can  be  reduced  to  some  physical 
principle.  It  is  indifferent  for  our  illustration  whether 
that  elementary  term  be  regarded  as  matter  or  energy,  so 
long  as  it  can  be  measured  and  its  exact  results  calculated. 
The  place  of  philosophy  and  of  all  the  sciences  would  then 
be  filled  by  a  universal  system  of  physics  which  would  be 
able  to  describe  and  explain  all  forms  of  existence  and  all 
changes  in  terms  of  its  own  principle.  Not  only  that,  but 
since  it  would  deal  with  a  strictly  determined  and  calculable 
series  of  events,  it  would,  theoretically  at  least,  be  able  to 
predict  all  occurrences  of  the  future,  both  mental  and  physi- 
cal alike,  down  to  the  smallest  detail.  More  than  a  century 
ago  Laplace  wrote:  "We  ought  then  to  regard  the  present 
state  of  the  universe  as  the  effect  of  its  antecedent  state, 
and  as  the  cause  of  the  state  that  is  to  follow.  An  intelli- 
gence who  for  a  single  instant  should  be  acquainted  with 
all  the  forces  by  which  nature  is  animated,  and  with  the 
several  positions  of  the  beings  composing  it,  if  further  his 
intellect  were  vast  enough  to  submit  these  data  to  analysis, 
would  be  able  to  include  in  one  and  the  same  formula  the 
movements  of  the  largest  bodies  in  the  universe,  and  those 
of  the  lightest  atom.     Nothing  would  be  uncertain  for  hina  ', 


39?  The  Unification  of  Knowledge 

the  future  as  well  as  the  past  would  be  present  to  his  eyes.' 
If  now,  as  we  are  assuming,  all  phenomena  are  in  the   last 
resort  reducible  to  some  physical  principle,  Laplace's  hy- 
pothetical calculator  would  also  be  omniscient  with  respect  to 
all  the  contents  of  every  mind  that  ever  existed  or  will  exist. 

The  assumption  that  mental  phenomena  are  at  bottom 
physical  in  character  —  special  forms  of  matter  or  energy  — 
may,  however,  appear  to  us  untenable.  It  may  appear 
that  experience  compels  us  to  take  a  Dualistic  hypothesis, 
and  to  assume  that  mental  events  form  an  independent 
series.  Nevertheless,  since  we  are  still  at  the  standpoint  of 
natural  science,  we  shall  find  in  this  field  also  causes 
and  effects.  This,  indeed,  is  what  we  must  assume  if  the 
natural  science  methods  of  description  and  explanation  are 
to  be  employed  in  psychology.  So  long  as  psychology  sets 
itself  the  task  of  regarding  mind  as  made  up  of  a  causally 
connected  series  of  events,,  so  long  must  every  mental  state 
be  regarded  as  capable  of  explanation  in  terms  of  some 
antecedent  process  or  processes.  There  can  be  no  state 
that  is  not  determined  or  conditioned  by  something  outside 
itself. 

Now  there  is,  perhaps,  at  first  sight  nothing  repugnant 
in  a  philosophy  which  interprets  the  external  world  as  a 
strictly  mechanical  series  of  causes  and  effects.  Further 
consideration  might,  indeed,  make  it  apparent  that,  if  this 
is  .the  ultimate  truth  regarding  the  physical  world,  the  mental 
life,  through  its  close  and  necessary  connection  with  the 
physical,  cannot  possess  any  real  freedom.  It  is,  however, 
with  the  natural  science  account  of  the  mental  life  itself 
that  discontent  first  arises.  The  physical  world,  we  are 
likely  to  feel,  may  be  mechanical:  indeed,  the  mechanical 


§  g6.    The  Assumptions  of  the  Sciences  399 

view  at  first  sight  seems  fairly  adequate  to  state  what  we 
know  regarding  its  behaviour.  But  the  psychological  inter- 
pretation of  mind  as  made  up  of  phenomena  which  are  all 
conditioned  externally,  conflicts  directly  with  our  ordinary 
beliefs  regarding  our  own  conscious  life,  and  that  of  our 
fellow-men.  If  the  causal  account  of  mind  is  ultimate, 
there  can,  of  course,  be  no  freedom  or  self-determination 
on  the  part  of  the  individual:  the  mind  is  simply  the  con- 
sciousness of  a  succession  of  states  which  are  strictly 
determined  in  the  order  and  mode  of  their  appearance. 
It  seems  extremely  difficult  to  reconcile  this  interpretation 
of  the  mental  life  with  what  we  demand  from  ourselves 
and  others  in  the  life  of  society,  as  well  as  with  the  sym- 
pathy and  interest  that  we  have  with  motives  and  acts  of 
historical  individuals.  The  scientific  view  of  mind,  as  made 
up  of  elements  which  are  conditioned  in  a  purely  mechanical 
way  in  their  mode  of  combination,  necessitates  a  fundamen- 
tally different  view  of  human  conduct  and  of  human  respon- 
sibility from  that  usually  entertained:  it  requires  us  to 
regard  our  own  conduct  and  that  of  our  fellow-men,  not  as 
subjects  of  praise  or  blame,  but  simply  as  phenomena  to  be 
understood.  This  is  the  philosophy  of  mind  and  of  human 
action  at  which  we  arrive  when  the  scientific  point  of  view 
is  regarded  as  the  final  interpretation. 

96.  The  Assumptions  of  the  Sciences.  —  The  possibility 
of  reaching  a  different  interpretation  of  the  world  and  of 
experience  from  that  afforded  by  natural  science  has  been 
more  than  once  suggested  in  the  preceding  paragraphs. 
It  has  never  been  shown,  however,  that  any  other  interpre- 
tation is  possible.  If  the  account  given  by  the  sciences  is 
true,  how  is  any  other  theory  possible?      Does  not  a  phi- 


400  The  Unification  of  Knowledge 

losophy  lose  all  title  to  respect  which  begins  by  proposing  to 
discredit  the  established  results  of  the  sciences? 

The  reply  to  these  objections  is  that  it  is  not  proposed  to 
question  the  competency  of  science  in  its  own  field;  but 
merely  to  show  that,  from  the  very  conditions  under  which 
it  is  formulated,  it  cannot  supply  an  answer  to  the  problems 
of  philosophy.  In  the  first  place,  the  inquiries  of  the  special 
sciences  are  not  directed  primarily  towards  the  discovery  of 
the  ultimate  relations  of  things.  Their  object  is  rather  to 
discover  some  method  of  describing  certain  groups  of  phe- 
nomena in  such  a  way  as  to  enable  others  to  apprehend 
them  readily  and  clearly.  With  this,  there  is  also  usually 
connected  the  practical  purpose  of  determining  how  the  phe- 
nomena can  be  produced  most  conveniently,  or  modified  in 
the  directions  we  may  desire.  Each  of  the  special  sciences, 
in  other  words,  takes  the  point  of  view  and  employs  the 
conceptions  which  will  enable  it  to  describe  most  conven- 
iently, in  accordance  with  its  own  purpose,  the  group  of 
phenomena  which  constitutes  its  subject-matter.  The  vari- 
ous conceptions  employed  have  sometimes  been  compared 
to  instruments  or  tools  which  enable  the  sciences  to  attain 
the  results  at  which  they  aim;  namely,  a  systematic  descrip- 
tion and  correlation  of  facts.  The  tests  of  these  conceptions 
from  the  scientific  point  of  view  is  found  simply  in  their 
efficiency,  or  in  their  capacity  to  afford  a  basis  for  clear 
description  and  for  practical  manipulation  of  the  phenomena 
under  investigation.  "All  physical  ideas  and  principles," 
says  Mach,  "are  succinct  directions,  frequently  involving 
subordinate  directions,  for  the  employment  of  economically 
classified  experiences,  ready  for  use.  Their  conciseness, 
as  also  the  fact  that  their  contents  are  rarely  exhibited  in 


§  96.    The  Assumptions  of  the  Sciences  401 

full,  often  invests  them  with  the  semblance  of  independent 
existence." l  Moreover,  what  is  here  said  regarding  the 
ideas  and  principles  of  physics  applies  equally  to  the  other 
sciences :  in  no  case  are  the  conclusions  derived  by  employing 
the  methods  and  assumptions  which  a  special  science  finds  ade- 
quate for  its  purpose  to  be  accepted  without  modification  or 
interpretation,  as  a  direct  description  of  the  nature  of  reality. 
The  matter  may  be  put  in  the  following  way.  All  think- 
ing proceeds  on  the  basis  of  certain  assumptions.  The  most 
general  form  of  these  assumptions  is  expressed  by  the  so- 
called  laws  of  thought  as  a  postulate  that  the  various  facts 
that  make  up  our  world  of  experience  are  to  be  related 
in  a  coherent  and  systematic  way.  Now,  there  are  various 
ways,  more  or  less  adequate,  and  more  or  less  final,  of  think- 
ing the  relations  of  things.  Although  each  of  the  natural 
sciences  makes  the  special  assumptions  which  enable  it  to 
deal  most  effectively  with  the  facts  in  its  own  field,  so  that 
its  form  of  explanation  always  differs  in  some  respect  from 
every  other,  yet  all  the  natural  sciences  make  certain  assump- 
tions in  common,  and  therefore  may  be  at  first  considered 
together  in  our  discussion.  The  general  nature  of  these 
assumptions  we  found  expressed  in  the  law  of  causality 
with  its  corollary,  the  conception  of  the  uniformity  of 
nature.  It  is  plain,  therefore,  that  the  conclusions  of 
all  these  sciences  is  in  a  sense  hypothetical,  rather  than 
categorical.  What  they  assert  is,  that  if  the  field  of  reality 
is  defined  as  composed  of  phenomena  external  to  one  another, 
but  standing  in  strict  causal  relations,  then  these  laws  and 
conceptions  appear  to  express,  more  adequately  than  any 
other,  the  relations  of  the  facts  when  read  from  that  point  of 

1  Popular  Scientific  Lectures,  p.  204. 
2D 


402  The  Unification  of  Knowledge 

view.  Statements  of  this  nature  are  obviously  not  intended 
to  be  absolute,  or  to  exclude  alternative  ways  of  interpreting 
the  facts.  The  character  of  the  results  is  evidently  con- 
ditioned by  the  initial  assumptions  of  the  whole  group  of 
natural  sciences. 

This  point  of  view  may  be  further  illustrated  by  consider- 
ing its  application  to  some  of  the  special  sciences.  Mathe- 
matics does  not  belong  to  the  causal  group  of  sciences  whose 
assumptions  we  have  considered;  but  its  hypothetical  and 
abstract  character  is  not  difficult  to  realize.  The  subject- 
matter  of  mathematics,  we  say,  is  not  any  actually  existing 
set  of  phenomena,  but  certain  ideally  simplified  forms  or 
relations  of  the  real  world.  The  straight  line,  or  the 
triangle,  for  example,  as  defined  by  geometry,  are  ideal 
conceptions,  or  hypotheses,  from  which  the  science  pro- 
ceeds to  deduce  the  consequences.  These  consequences 
are  not  taken  as  direct  descriptions  of  the  physical  world, 
though  they  illustrate  certain  phases  or  aspects  of  that 
world.  If  now  we  turn  to  physics,  we  find  that  the  char- 
acter of  the  results  is  determined  in  the  same  way,  though 
not  to  the  same  degree,  by  the  initial  definitions  and  hypoth- 
eses of  the  science.  In  order  to  be  able  to  deal  with  the 
changing  and  almost  infinite  variety  of  the  physical  world, 
it  is  necessary  to  adopt  and  carefully  define  certain  concep- 
tions, such  as  space,  time,  energy,  atom,  ether,  etc.  It 
then  becomes  the  problem  of  physics  to  represent  all  the  mani- 
fold phenomena  of  the  external  world  as  determinate  rela- 
tions between  these  conceptions.  The  choice  of  these  con- 
ceptions is  determined  by  their  capacity  to  correlate  facts, 
and  to  serve  as  instruments  of  investigation.  In  the  prog- 
ress of  the  science,  a  constant  working  over  and  redefining 


§  g6.    The  Assumptions  of  the  Sciences  403 

of  the  working  hypotheses  goes  on,  the  attempt  being  always 
to  reach  conceptions  that  will  be  more  effective  as  instru- 
ments of  investigation,  and  at  the  same  time  permit  of  the 
description  of  phenomena  in  more  concrete  terms. 

It  follows,  then,  that  the  working  conceptions  of  physics, 
no  more  than  the  working  conceptions  of  mathematics,  are 
exact  descriptions  of  concretely  existing  things.  They  are 
ideally  simplified  conceptions,  adopted  and  defined  as  effec- 
tive instruments  for  dealing  with  the  physical  world  for 
certain  purposes.  These  conclusions  are  at  the  present 
time  recognized  by  physicists  who  are  interested  in  the  logical 
interpretation  of  their  results  as  well  as  by  philosophers. 
A  parallel  to  the  following  passage  from  Mach  may  readily 
be  found  in  the  writings  of  many  other  writers :  "  When  a 
geometer  wishes  to  understand  the  form  of  a  curve,  he  first 
resolves  it  into  small  rectilinear  elements.  In  doing  this, 
however,  he  is  fully  aware  that  these  elements  are  only  pro- 
visional and  arbitrary  devices  for  comprehending  in  parts 
what  he  cannot  comprehend  as  a  whole.  .  .  .  Similarly, 
it  would  not  be  right  for  physical  science  to  regard  its 
self-created,  changeable,  economical  tools, — the  molecules 
and  atoms  —  as  realities  behind  phenomena  ...  the  atom 
must  be  regarded  as  a  tool  for  representing  phenomena, 
like  the  functions  of  mathematics.  Gradually,  however, 
as  the  intellect,  by  contact  with  its  subject-matter,  grows 
in  discipline,  physical  science  will  give  up  its  mosaic  play 
with  stones  and  will  seek  out  the  boundaries  and  forms  of 
the  bed  in  which  the  living  stream  of  phenomena  flows. 
The  goal  which  it  has  set  itself  is  the  simplest  and  most 
abstract  expression  of  facts."  * 

1  Op.  cit.,  p.  206. 


404  The  Unification  of  Knowledge 

In  the  opening  chapter  of  this  book  (p.  9)  it  was  stated 
that  at  the  present  time  an  important  difference  of  opinion 
exists  as  to  the  proper  standpoint  and  working  conceptions 
of  the  science  of  psychology.  Functional  psychology  at- 
tempts to  employ  the  principle  of  purpose  or  adaptation 
as  its  principle  of  analysis  and  explanation.  Structural 
psychology,  on  the  other  hand,  following  more  strictly  the 
methods  of  the  other  natural  sciences,  describes  and  explains 
mental  life  in  terms  of  causally  related  elements.  It  is 
this  latter  view  of  mind,  when  accepted  without  modifi- 
cation as  a  philosophical  theory,  to  which  attention  is 
called  in  the  last  section.  When  we  reflect  on  the  meaning 
of  the  results  obtained  by  the  natural  science  method  of 
procedure  in  psychology,  it  becomes  evident  that  these 
cannot  be  regarded  as  furnishing  a  final  or  categorical 
account  of  the  real  character  of  the  mental  life.  For,  as  in 
the  case  of  physics,  their  form  is  due  to  the  nature  of  the 
assumptions  adopted  by  the  science.  The  concrete  mental 
life,  as  we  know  it  in  our  experience,  is  a  life  directed  more 
or  less  consciously,  and  more  or  less  consistently,  to  the 
attainment  of  certain  ends.  To  live  as  conscious  beings 
means  to  have  purposes,  to  will  certain  results,  and  employ 
ourselves  in  such  a  way  as  to  bring  about  their  attainment. 
Without  the  conception  of  the  mind  as  a  system  of  func- 
tions, engaged  in  realizing  certain  ends,  mental  life  appears 
unmeaning,  both  from  the  standpoint  of  ordinary  experience, 
and  also  from  that  of  sciences  like  history,  ethics,  and  logic. 
Now,  psychology  undertakes,  in  the  interest  of  exact  de- 
scription, to  exhibit  this  mental  life  as  a  series  of  causally 
conditioned  phenomena,  possessing  certain  definitely  ascer- 
tainable  characteristics,    and    taking   place    in    accordance 


§  97-    Philosophy  as  the  Interpretation  of  the  Sciences    405 

with  certain  laws.  In  looking  at  the  mental  life  as  made  up 
merely  of  a  series  of  states  to  be  described,  psychology  neces- 
sarily has  to  abstract  from  the  function  or  work  of  mind.  It 
deals  only  with  a  certain  phase  of  mind ;  or  it  may  be  said 
that  its  results  are  true  only  of  one  side  or  aspect  of  the 
total  mental  life.  As  science,  its  results  are  true  and  satis- 
factory if  they  adequately  fulfil  the  purposes  of  the  psy- 
chologist. It  is  only  when  they  are  mistaken  for  philosophy 
that  they  become  false  and  misleading.  Psychology,  as 
Professor  Muensterberg  has  remarked,  "must  not  be  trans- 
formed into  Psychologism.  In  the  preface  to  his  book 
entitled  Psychology  and  Life  the  same  author  writes :  "Pop- 
ular ideas  about  psychology  suggest  that  the  psychological 
description  and  explanation  of  mental  facts  expresses  the 
reality  of  our  inner  experience.  It  is  a  natural  consequence 
of  such  a  view  that  our  ethical  and  assthetical,  our  practical 
and  educational,  our  social  and  historical  views  are  sub- 
ordinated to  the  doctrines  of  psychology.  These  papers 
endeavour  to  show  that  psychology  is  not  at  all  an  expression 
of  reality,  but  a  complicated  transformation  of  it,  worked 
out  for  special  logical  purposes  in  the  service  of  our  life. 
Psychology  is  thus  a  special  abstract  construction  which 
has  a  right  to  consider  everything  from  its  own  important 
standpoint,  but  which  has  nothing  to  assert  in  regard  to 
the  interpretation  and  appreciation  of  our  real  freedom 
and  duty,  our  real  values  and  ideals." 

§  97.  Philosophy  as  the  Interpretation  of  the  Sciences.  — 
The  work  of  philosophy  is,  however,  not  fulfilled  in  simply 
showing  that  there  is  no  finality  in  the  conclusions  of  the 
special  sciences:  there  is  still  demanded,  as  we  have  seen, 
such  an  interpretation  of  the  various  facts  of  experience  as 


406  The  Unification  of  Knowledge 

will  render  possible  some  coherent  view  of  the  nature  of  the 
world  as  a  whole.  Now  into  this  construction  the  results 
of  the  special  sciences  must,  in  some  way,  enter.  These 
results,  as  has  been  shown,  are  hypothetical,  abstract,  and 
incomplete  in  character,  but  they  are  not  arbitrary  or  capri- 
cious. Although  they  cannot  be  taken  as  directly  or  cate- 
gorically descriptive  of  concrete  things,  scientific  proposi- 
tions do  illustrate  certain  general  phases  or  aspects  of  both 
physical  and  mental  experience,  and  are  therefore  significant 
for  philosophy.  To  understand  what  they  really  assert,  then, 
it  is  essential  to  comprehend  the  limitations  and  conditions 
which  the  postulates  of  the  field  from  which  they  are  derived 
impose  upon  them.  It  is  only  by  making  clear  their  assump- 
tions that  their  true  import  and  significance  can  be  brought 
to  light. 

When  this  has  been  done,  the  further  problem  will  remain 
as  to  what  category  or  conception  is  most  adequate  to  express 
the  relations  of  all  of  the  various  parts  of  the  world  of  expe- 
rience. What  is  the  highest  or  final  category  of  thought 
which  will  prove  adequate  to  the  complete  unification  of 
knowledge?  It  is  clear  that  the  conception  which  phi- 
losophy aims  to  define  would  only  be  adequate,  if  it  included 
within  itself,  as  relative  or  partial  truths,  the  results  obtained 
by  the  investigations  of  the  other  sciences.  Or,  in  other 
words,  while  each  of  the  special  sciences,  limiting  itself, 
as  it  must,  to  the  investigation  of  a  particular  part  of  the 
world,  is  never  able  to  obtain  the  full  and  final  truth  about 
that  part,  its  results  are  never  without  significance  for  an 
ultimate  synthesis.  Indeed,  it  is  only  by  making  use  of  the 
work  of  the  sciences  that  philosophy  is  able  to  advance  to  a 
more  comprehensive  interpretation.     On  the  other  hand, 


§  97-    Philosophy  as  the  Interpretation  of  the  Sciences    407 

the  sciences  are  aided  in  their  work  of  interpreting  special 
groups  of  phenomena  by  philosophical  conceptions  regard- 
ing the  meaning  and  bearing  of  their  special  results.  The 
ultimate  postulate  of  our  thought  being  that  the  universe 
is  systematic  and  coherent,  the  part  can  only  be  fully  compre- 
hended when  it  is  seen  in  the  light  of  the  whole. 

The  history  of  philosophy  may  be  read  as  an  account  of 
the  attempts  made  by  the  human  race  to  find  a  conception, 
or  category,  adequate  to  unify  all  the  facts  of  experience. 
Beginning  with  the  childlike  idea  that  everything  must 
be  composed  of  the  same  kind  of  stuff  or  matter,  philo- 
sophical thought  quickly  advanced  to  more  rational  state- 
ments of  its  problem.  At  the  present  time,  one  may  perhaps 
say  that  the  fundamental  question  in  philosophy  is  whether 
it  is  possible  to  employ  the  category  of  Teleology  or  Purposive- 
ness  as  an  explanation  of  the  universe  and  of  our  own  expe- 
rience; and,  if  so,  what  content  is  to  be  given  to  this  concep- 
tion. We  have  noted  the  fact  that  an  explanation  in  causal 
terms  leads  necessarily  to  an  infinite  regress  (cf.  p.  371), 
as  well  as  the  other  difficulties  that  arise  when  this  category 
is  taken  as  ultimate.  The  question  then  is:  Are  we  jus- 
tified in  advancing  to  a  different  form  of  judgment,  to  judg- 
ments of  Teleology  or  Individuality?  (Cf.  p.  370.)  If 
this  question  be  answered  in  the  affirmative,  it  is  above  all 
essential  to  remember  that  a  change  of  category  is  no  excuse 
for  indefiniteness.  Philosophical  analysis  and  interpreta- 
tion are  necessarily  different  from  those  of  science,  but 
philosophical  procedure  must  not  be  less  strict  than  that  of 
the  sciences,  or  its  conceptions  less  carefully  defined. 


408  The  Unification  of  Knowledge 

REFERENCES 

H.  Muensterberg,  Psychology  and  Life,  1899. 
"  "  The  Eternal  Values,  1909. 

James  Ward,  Naturalism  and  Agnosticism,  2d  edition,  1903,  espe* 
daily  Lectures  II.-VI.  and  XIX. 

E.  Mach,  Popular  Scientific  Lectures. 

J.  E.  Creighton,  "  Methodology  and  Truth,"  Philos.  Review,  Vol. 

X.,  pp.  45  ff- 

E.  Albee,  "  The  Significance  of  Methodological  Principles,"  Philos. 
Review,  Vol.  XV.,  pp.  267  ff.  ;  "  Descriptive  and  Normative  Sciences," 
Ibid.,  Vol.  XVI.,  pp.  40  ff. 


QUESTIONS   AND   EXERCISES 

INTRODUCTION 

Chapter  I.  —  The  Standpoint  and  Problem  of  Logic 

i.  What  are  some  of  the  main  characteristics  of  thought  or 
thinking?  Explain  the  distinction  between  a  subjective  and  an 
objective  account  of  thought. 

2.  Explain  the  use  of  the  verb  to  think  in  each  of  the  following 
sentences:  'I  do  not  know,  but  I  think  so;'  'If  you  think  the 
matter  over,  you  will  come  to  the  same  conclusion.' 

3.  'Words  and  phrases  are  often  repeated  without  reflection,  and 
their  very  familiarity  is  likely  to  prevent  us  from  attempting  to 
understand  exactly  what  ideas  they  represent.'  Give  illustra- 
tions of  this  fact. 

4.  What  do  you  mean  by  science?  How  does  'scientific' 
knowledge  differ  from  the  knowledge  of  ordinary  life? 

5.  What  is  the  meaning  of  the  word  'law'  in  the  phrase  'a  law 
of  thought'?  Compare  the  use  of  the  word  in  such  expressions 
as  'laws  of  nature,'  'the  laws  of  the  land.' 

6.  Is  it  true  that  Logic  and  Psychology  have  the  same  subject- 
matter  ? 

7.  Explain  carefully  how  the  problem  of  Logic  differs  from 
that  of  Psychology. 

8.  If  we  parallel  Psychology  with  Morphology,  and  Logic 
with  Physiology,  what  mental  science  will  correspond  to  Em- 
bryology ? 

9.  Illustrate  by  means  of  examples  not  used  in  the  text  the  rela- 
tion in  which  science  and  art,  or  theory  and  practice,  stand  t« 
each  other. 

409 


410  Questions  and  Exercises 

10.  Criticise  the  following  statement:  'Logic  is  not  only  a 
science;  it  is  also  an  art,  for  it  teaches  us  to  reason  correctly.' 

ii.  What  part  does  Introspection  play  in  investigating  logical 
questions  ? 

12.  In  what  sense  is  Logic  a  '  normative'  science?  Name  other 
sciences  that  are  'normative.' 

13.  In  what  sense  may  we  say  that  the  records  of  everything 
which  the  human  race  has  accomplished  form  the  material  of 
Logic  ?    How  does  the  individual  mind  deal  with  this  material  ? 

Chapter  II.  —  Stages  in  the  Development  of  Logic 

1.  What  form  did  the  questions  concerning  the  nature  of  know- 
ledge first  take  ?  Under  what  conditions  did  these  first  receive  defi- 
nite formulation? 

2.  'The  sciences  have  arisen  in  response  to  the  practical  needs 
of  mankind.'  Is  this  statement  confirmed  by  the  history  of  the 
origin  and  development  of  Logic? 

3.  'Since  each  individual  sees  things  from  his  own  point  of 
view,  there  is  therefore  nothing  really  true  in  itself,  or  good  in 
itself.'  Give  some  illustrations  of  the  former  part  of  this  state- 
ment. What  term  would  you  use  to  describe  the  theory  which 
the  sentence  expresses? 

4.  Explain  what  is  meant  by  the  statement  that  Socrates  and 
Plato  found  a  standard  of  truth  and  of  conduct  in  the  Concept. 

5.  Why  was  it  not  possible  for  Aristotle  to  lay  down  a  complete 
theory  of  Inductive  Reasoning? 

6.  Describe  the  attitude  toward  Logic  during  the  Middle  Ages. 
How  can  this  be  accounted  for? 

7.  What  is  meant  by  Bacon's  'method'?  In  what  does  its 
value  consist? 

8.  Describe  Mill's  services  to  Logic,  also  the  defects  in  his 
view  of  experience. 

9.  Describe  the  standpoint  of  Modern  Logic. 


Questions  and  Exercises  41 1 

PART    I. —  The  Syllogism 
Chapter  III.  —  The  Syllogism  and  its  Parts 

1.  Describe  the  general  purpose  and  nature  of  the  syllogism. 

2.  What  is  the  principle  upon  which  syllogistic  reasoning 
depends?  Why  is  it  impossible  to  reason  if  this  principle  be 
violated  ? 

3.  Explain  the  distinction  between  the  formal  and  real  truth  of 
an  argument. 

4.  Explain  the  distinction  between  a  Percept  and  a  Concept. 

5.  What  is  meant  by  the  transforming  and  the  conserving 
functions  of  thought?  What  part  does  language  play  in  the 
process  of  thinking? 

6.  Arrange  the  following  sentences  as  logical  propositions, 
pointing  out  the  logical  Subject  and  the  Predicate  in  each  case:  — 

(a)  Learning  taketh  away  the  wildness  of  men's  minds. 

(b)  Dissipation  wastes  health. 

(c)  The  exposition  of  a  principle  indirectly  contributes  to 

its  proof. 

(d)  To  me  the  meanest  flower  that  lives  can  give  thoughts 

that  do  often  lie  too  deep  for  tears. 

(e)  The  Alps  consist  of  several  parallel  ranges. 
(J)  The  travellers  had  found  the  city  in  ruins. 

7.  In  the  following  examples,  the  student  is  required  (1)  to  state 
the  arguments  in  syllogistic  form,  rearranging  them  if  necessary 
in  the  order  of  Major  Premise,  Minor  Premise,  and  Conclusion; 
(2)  to  supply  missing  premises  or  conclusions,  or  to  condense, 
where  several  statements  really  constitute  one  proposition;  (3)  to 
state  whether  the  argument  seems  to  be  valid: — ■ 

(1)  He  is  not  indifferent  to  money;    for  he  is  a  sensible  man, 

and  no  sensible  man  despises  money. 

(2)  All  human  productions  are  liable  to  error,  and  therefore 

all  books,  being  human  productions,  are  liable  to  error, 


412  Questions  and  Exercises 

(3)  All  that  glitters  is  not  gold;   for  brass  glitters. 

(4)  All  bodies  which  move  round  the  sun  are  planets;  there 

fore  the  earth  is  a  planet. 

(5)  Platinum  is  a  metal,  and  therefore  combines  with  oxygen. 

(6)  Every  honest  man  attends  to  his  business;    this  person 

attends  to  his  business;  therefore  this  person  is  an 
honest  man. 

(7)  Rational  beings  are  accountable  for  their  actions;  brutes, 

not  being  rational,  are  therefore  exempt  from  re- 
sponsibility. 

(8)  I  am  not  mortal,  for  I  have  obtained  the  Elixir  Vita. 

(9)  Of  vourse  he  defends  State  Rights,  for  he  is  a  Southerner. 

(10)  The  poor  must  be  oppressed,  for  the  rich  are  accumulat- 

ing millions. 

(11)  These  men  are  traitors,  for  they  oppose  the  President. 

(12)  It  cannot  be  said  that  no  impractical  man  is  a  politician, 

for  some  politicians  are  idealists,  and  no  idealist  is  prac- 
tical. 

(13)  Phenomena  attributed  by  savages  to  the  existence  of  spirits 

are  fully  capable  of  explanation  by  science  without  this 
hypothesis,  therefore  the  hypothesis  ought  to  be  entirely 
discarded. 

(14)  Neglect  of  pleasure  is  the  best  way  to  secure  it;    for  the 

more  we  aim  at  pleasure,  the  less  likely  we  are  to  get  it. 

(15)  Restless  nations  are  not  progressive,  for  we  see  that  the 

civilized  nations  are  all  progressive,  while  all  the  un- 
civilized nations  are  restless. 

(16)  Any  citizen  may  rightly  resist  a  law  of  which  his  reason 

disapproves,  for  every  man  is  in  duty  bound  to  follow 
the  dictates  of  his  reason. 

(17)  Materialism  is  refuted  by  the  fact  that,  while  all  man's 

material  qualities  may  be  transmitted  by  inheritance, 
his  knowledge   cannot. 


Questions  and  Exercises  4 1 3 

(18)  Every  one  desires  money,  because  every  one  desires  power 

(19)  We  must  not  give  in  to  him,  for  if  you  give  him  an  inch,  hi 

will  take  an  ell. 

(20)  Covetous  men  are  not  happy,  seeing  that  they  are  always 

in  fear. 

(21)  The  example  of  Virgil  shows  that  a  great  poet  may  be 

led  into  some  faults  by  the  practice  of  imitation. 

(22)  You  must  have  met  him,  for  you  were  at  the  university  at 

the  same  time. 

(23)  No  strike  but  injures  trade,  and  consequently  impover- 

ishes the  country.  But  this  is  to  diminish  the  means  of 
happiness.  And  as  all  that  is  detrimental  to  happiness 
is  to  be  condemned,  we  must  absolutely  condemn  strikes. 

(24)  This  document  cannot  be  genuine,  or  it  would  have  been 

referred  to  by  the  supposed  author's  contemporaries. 

(25)  This  is  too  good  to  be  true. 

(26)  It  is  inconceivable  that  the  material  world  should  be  per- 

ceived, since  we  can  only  perceive  that  which  lies 
within  consciousness. 

(27)  A  great  chess-player  is  not  a  great  man,  for  he  leaves  the 

world  as  he  found  it. 

(28)  It  is  a  mistake  to  improve  the  economic  condition  of  the 

inefficient,  so  we  ought  not  to  assist  the  destitute. 

(29)  B  is  so  bad  a  marksman  that  the  safest  place  to  stand  is 

directly  in  front  of  the  bull's-eye.     (12-29  St.  Andrew's.) 

(30)  He  is  already  rich  and  powerful,  so  that  he  cannot  be  guilty 

of  usury  and  extortion. 

(31)  Years  bring  wisdom,  but  you  are  still  young.     (30-31 

Glasgow.) 

(32)  The  man  I  don't  like  is  the  man  I  don't  know. 

(33)  One  belated  diversion  the  high-tariff  people  are  now  trying 

to  make.  They  betray  a  sudden  anxiety  about  the 
revenue.  .  .  .     But  the  moment  you  begin  to  talk  of 


414  Questions  and  Exercises 

the  tariff  as  needed  for  revenue,  that  moment  yoii 
abandon  the  protectionist  point  of  view.  To  fix  the 
duties  at  a  level  where  they  would  produce  the  greatest 
revenue  is  a  process  which  has  nothing  to  do  with  pro- 
tection. Instead  of  keeping  up  the  rates  for  the  pur- 
pose of  bringing  in  more  money,  the  true  way  might  be 
to  cut  them  in  two. 

(34)  In  this  country  we  yet  have  a  hard  road  to  travel  before  we 

reach  free  trade,  or  even  the  nearer  stage  of  a  tariff 
for  revenue  only.  We  are  and  shall  remain  large 
producers  of  grain  and  meat;  and  it  is  therefore  un- 
likely that  we  shall  be  driven  to  free  trade,  as  England 
was,  by  the  pangs  of  the  millions.  The  economic  ar- 
gument is  still  irrefutable;  but,  while  men  are  earn- 
ing a  fair  wage,  are  fed,  and  comfortably  clad  and 
housed,  they  are  indifferent  to  general  principles.  Too 
many  of  us  hear  only  the  cry  of  the  belly. 

(35)  No  human  being  in  this    country  can  exercise  any  kind 

of  public  authority  which  is  not  conferred  by  law;  and 
under  the  law  of  the  United  States  it  must  be  given 
by  the  express  words  of  a  written  statute.  Whatever  is 
not  so  given  is  withheld,  and  the  exercise  of  it  is  posi- 
tively prohibited.  Courts-martial  in  the  army  and  navy 
are  authorized ;  they  are  legal  institutions;  their  jurisdic- 
tion is  limited,  and  their  whole  code  of  procedure  is 
regulated  by  act  of  Congress.  Upon  the  civil  courts 
all  the  jurisdiction  they  have  or  can  have  is  bestowed 
by  law,  and  if  one  of  them  goes  beyond  what  is  written, 
its  action  is  ultra  vires  and  void.  But  a  military  com- 
mission is  not  a  court-martial,  and  it  is  not  a  civil 
court.  It  is  not  governed  by  the  law  which  is  made 
for  either,  and  has  no  law  of  its  own.  ...  So  these 
commissions  have  no  legal   origin  and  no  legal  name 


Questions  and  Exercises  415 

by  which  they  are  known  among  the  children  of  men; 
no  law  applies  to  them,  and  they  exercise  all  power  for 
the  paradoxical  reason  that  none  belongs  to  them 
rightly.     (J.  S.  Black.) 

(36)  Has  (the  constitution)  empowered  Congress  to  enact 
what  free  persons,  born  within  the  several  states,  shall 
or  shall  not  be  citizens  of  the  United  States  ?  Before 
examining  the  various  provisions  of  the  constitution 
which  may  relate  to  this  question,  it  is  important  to 
consider  for  a  moment  the  substantial  nature  of  this 
inquiry.  It  is,  in  effect,  whether  the  constitution  has 
empowered  Congress  to  create  privileged  classes  within 
the  states,  who  alone  can  be  entitled  to  the  franchises 
and  powers  of  citizenship  of  the  United  States.  If  it 
be  admitted  that  the  constitution  has  enabled  Congress 
to  declare  what  free  persons,  born  within  the  several 
states,  shall  be  citizens  of  the  United  States,  it  must 
at  the  same  time  be  admitted  that  it  is  an  unlimited 
power.  If  this  subject  is  within  the  control  of  Congress, 
it  must  depend  wholly  on  its  discretion.  For  certainly 
no  limits  of  that  discretion  is  found  in  the  constitu- 
tion, which  is  wholly  silent  concerning  it;  and  the  nec- 
essary consequence  is  that  the  federal  government  may 
select  classes  of  persons  who  alone  can  be  entitled  to 
the  political  privileges  of  citizenship  of  the  United 
States.  If  this  power  exists,  what  persons  born  within 
the  states  may  be  president  or  vice-president  of  the 
United  States,  or  members  of  either  house  of  Congress, 
or  hold  any  office  or  enjoy  any  privilege  whereof  citi- 
zenship of  the  United  States  is  a  necessary  qualifica- 
tion, must  depend  solely  on  the  will  of  Congress.  By 
virtue  of  it  .  .  .  Congress  .  .  .  may  create  an  oli- 
garchy, in  whose  hands  would  be  concentrated  the  en« 


41 6  Questions  and  Exercises 

tire  power  of  the  federal  government.  .  .  .  Certainly, 
we  ought  to  find  this  power  granted  by  the  constitution, 
at  least  by  some  necessary  inference,  before  we  can  say 
it  does  not  remain  to  the  states  or  the  people.  (B.  R. 
Curtis.) 

Chapter  IV.  —  Terms 

i.  Distinguish  in  the  following  list  the  terms  which  are  usually 
(i)  Singular,  (2)  General,  and  (3)  Collective.  If  any  term  may 
belong  to  more  than  one  class,  explain  and  illustrate  its  various 
uses. 

Niagara  Falls,  an  oak  tree,  the  United  States  Navy, 

gold,  a  dancing  party,  Brooklyn  Bridge, 

chair,  the  United  States,  humanity, 

a  pack  of  cards,  city,  the  centre  of  the  earth. 

2.  Explain  and  illustrate  the  ambiguity  in  the  use  of  the  word 
'all.' 

3.  In  what  two  ways  are  the  words  Abstract  and  Concrete 
used?  In  what  sense,  if  at  all,  can  we  say  that  Psychology  and 
Logic  are  'abstract'  sciences? 

4.  What  do  you  think  that  Hegel  meant  when  he  said  that  "it 
is  the  uneducated  man  who  thinks  abstractedly"? 

5.  Distinguish  carefully  between  Contradictory  and  Opposite 
terms. 

6.  What  are  Correlative  terms?      Give  at  least  three  examples. 

7.  Mention  the  synonyms  for  Intension  and  Extension. 

8.  Explain  the  Extensional  and  Intensional  use  of  the  following 
terms :  — 

metal,  chair,  man,  Caesar,  superstition, 

justice,  student,  John  Jones,  island,  emperor. 

9.  Criticise  the  statement  that  'Extension  and  Intension  stand 
?n  inverse  ratio  to  each  other.'     What  truth  does  it  contain'; 


Questions  and  Exercises  417 

10.  Invent  a  series  of  at  least  six  terms  which  may  be  arranged 
so  as  gradually  to  increase  in  Extension. 

11.  What  may  be  said  in  reply  to  Mill's  contention  that  proper 
names  are  non-connotative  ? 

Chapter  V.  —  Definition  and  Division 

1.  Why  is  Definition  necessary? 

2.  What  is  the  distinction  between  extensive  and  intensive 
definition  ?     What  is  a  verbal  definition  ? 

3.  In  what  two  ways  may  we  conceive  the  problem  of  Definition  ? 

4.  What  do  you  understand  by  the  Socratic  Dialectic?  Ex- 
plain its  purpose  and  mode  of  procedure. 

5.  Explain  the  terms:  — 

genus,  differentia,  infirma  species, 

species,  summum  genus,  sui  generis. 

6.  What  various  methods  or  kinds  of  definition  can  you  dis- 
tinguish? What  is  it  which  determines  which  method  shall  be 
used  in  any  particular  case  ?     What  is  genetic  definition  ? 

7.  Criticise  the  following  definitions,  pointing  out  what  rules, 
if  any,  are  violated  by  them,  and  distinguishing  genus  and  differen- 
tia, if  possible,  in  each  :  — 

(1)  Logic  is  the  science  of  thought. 

(2)  A  power  is  a  force  which  tends  to  produce  motion. 

(3)  Tin  is  a  metal  lighter  than  gold. 

(4)  A  gentleman  is  a  man  who  has   no   definite    means   of 

support. 

(5)  The  body  is  the  emblem  or  visible  garment  of  the  soul. 

(6)  Man  is  a  vertebrate  animal. 

(7)  Thunder-bolts  are  the  winged  messengers  of  the  gods. 

(8)  A  moral  man  is  one  who  does  not  lie   or   steal  or  live 

intemperately. 

(9)  Cheese  is  a  caseous  preparation  of  milk. 

(10)  Evolution  is  to  be  defined  as  a  continuous  change  from 
2  E 


418  Questions  and  Exercises 

indefinite  incoherent  homogeneity  to  definite  coherent 
heterogeneity  of  structure  and  function,   through   suc- 
cessive differentiations  and  integrations.     (Spencer.) 
(n)  Oats  is  a  grain  which   in   England  is  generally  given  to 
horses,  but  in  Scotland  supports  the  people. 

(12)  Tickling  may  be  defined  as  an  intensely  vivid  complex  of 

unsteady,  ill-localized,  and  ill-analyzed  sensation,  with 
attention  distributed  over  the  immediate  sensory  con- 
tents and  the  concomitant  sensations  reflexly  aroused. 

(13)  Panmixia  is  the  fact  that  "  natural  selection  is  required  to 

preserve  an  organ  in  an  active  condition  as  well  as  to 
produce  it,  and  if  this  action  is  withdrawn,  the  organs 
will  degenerate  from  promiscuous  breeding." 

(14)  Belief  is  the  consequence  of   an  indissoluble  association 

of  ideas. 

(15)  Life  is  the  opposite  of  death. 

(16)  Reverence  is  the  feeling  produced  by  the  recognition  of 

worth  or  superiority  in  others. 

(17)  Religion  consists  in  the  feeling  of  absolute  dependence. 

(Schleiermacher.) 

(18)  Religion   is   a    desire    manifested    by    prayer,   sacrifice. 

and  faith.     (Feuerbach.) 

(19)  Religion  is  the  sentiment  aroused  by  regarding   duty   as 

based  on  a  divine  command.     (Kant.) 

(20)  Religion  is  a  faculty  of  the  mind  by  which,  independently 

of  the  senses  and  of  reason,  man  is  able  to  perceive 
the  Infinite.     (Max  Muller.) 

(21)  Religion,  in  its  lowest  terms,  is   the   belief   in   spiritual 

beings.     (Tylor.) 

(22)  Material  Goods  consist   of   useful    material    things,  and 

of  all  rights  to  hold,  or  use,  or  derive  benefits  from  ma- 
terial things,  or  to  receive  them  at  a  future  time. 
(Marshall.) 


Questions  and  Exercises  419 

(23)  A  man's  Wealth  consists  of  (i)  those  Material  Goods  to 

which  he  has  (by  law  or  custom)  private  rights  of  prop- 
erty, and  which  are  therefore  transferable  and  exchange- 
able; and  of  (ii)  those  of  his  Immaterial  Goods  which 
are  external  to  him,  and  serve  directly  as  the  means  of 
enabling  him  to  acquire  Material  Goods.      (Marshall.) 

(24)  Or,  Wealth  includes  all  those  things,  external  to  a  man, 

which  (1)  belong  to  him,  and  do  not  belong  equally  to 
his  neighbours,  and  therefore  are  distinctly  his;  and 
(2)  which  are  directly  capable  of  a  money  measure. 
(Ibid.) 

(25)  A  person's  capital  is  that  part  of  his  stock  from  which  he 

expects  to  derive  an  income.     (A.  Smith.) 

(26)  A  person's  capital  is  that  portion  of  his  wealth  by  which 

he  earns  his  livelihood.     (Marshall.) 

(27)  Capital  is  the  accumulation  of  all  that  is  valuable  which 

has  been  withdrawn  from  unproductive  consumption^ 
(Say.) 

(28)  Capital  is  that  portion  of  the  produce  of  industry  which 

can  be  made  directly  available  to  support  human  exist- 
ence or  to  facilitate  production.     (M'Culloch.) 

(29)  Capital  is  something  produced,  for  the  purpose  of  being 

employed  as  the  means  toward  a  further  production. 
(Mill.) 

(30)  Rent  is  what  is  paid  for  the  license  to  gather  the  produce 

of  the  land.     (Smith.) 

(31)  Rent  is  that  portion  of  the  produce  of  the  earth  which  is 

paid  by  the  farmer  to  the  landlord  for  the  use  of  the 
natural  and  inherent  powers  of  the  soil.     (M'Culloch.) 

(32)  Rent  is  the  difference   between   the  return  made  to  the 

most  productive,  and  that  which  is  made  to  the  least 
productive,  portion  of  capital  employed  on  the  land. 
(Mill.) 


420  Questions  and  Exercises 

(33)  Rent  is  the  income  derived  from  the  ownership  of  land 

and  other  free  gifts  of  nature.     (Marsha!!.) 

(34)  Wages  is  the  price  of  labour.     (Smith  and  many  others.) 

(35)  Labour  is  any  exertion  of  mind  or  body  undergone  partly 

or  wholly  with  a  view  to  some  good  other  than  the 
pleasure  derived  directly  from  the  work.      (Marshall.) 

(36)  Vestigial  characters  in  animals  are  the  remnants  of  past 

adaptations. 

(37)  "By  isolation,  segregation,  or  separation   as  a  factor  in 

evolution,  we  mean  the  failure  of  a  portion  of  one  group 
or  species  to  interbreed  freely  with  the  rest  of  its  kind." 
(Jordan.) 

8.  Give  examples  of  terms  which  are  indefinable,  and  explain 
why  this  is  the  case.  What  is  the  distinction  between  Descrip- 
tion and  logical  Definition? 

9.  Define  the  following  terms  by  giving  the  genus  and  differ- 
entia: — 

science,  republic,  psychology,  island, 

triangle,  monarchy,  gold  standard,  import  duty. 

10.  Define  the  following  terms  in  whatever  way  seems  most 
suitable  and  satisfactory :  — 


organism, 
Natural  Selection, 

cantilever  bridge, 
book, 

oxygen, 
indigo  blue, 

steel, 

surd  number. 

tyranny, 
tort, 

parabola, 
Communism, 

torsion, 
pain, 

Can  any  of  these  be  defined  in  more  than  one  way? 
11.  Examine  the  following  Divisions  and  point  out  which  are 
logical  and  which  are  not:  — 

(1)  Living  beings  into  moral  and  immoral. 

(2)  Men  into  saints  and  sinners. 

(3)  Religions  into  true  and  false. 

(4)  Man  into  civilized  and  black. 


Questions  and  Exercises  421 

(5)  Geometrical    figures   into   rectilinear   and   non-rectilin- 

ear. 

(6)  Substances  into  material  and  spiritual. 

(7)  Metals  into  white,  heavy,  and  precious. 

(8)  Elementary  mental  processes  into  sensations  and  affec- 

tions. 

(9)  Students  into  those  who  are  idle,  those  who  are  athletic, 

and  those  who  are  diligent. 
(10)  Books  into  scientific  and  non-scientific. 

Chapter  VI.  —  Propositions 

1.  What  is  a  proposition  ?  In  what  sense  may  a  proposition 
be  said  to  have  parts  ? 

2.  Distinguish  between  Categorical  and  Conditional  propo- 
sitions. 

3.  What  is  meant  by  (a)  the  Quality,  and  (b)  the  Quantity,  of 
propositions  ? 

4.  Arrange  the  following  sentences  in  the  form  of  logical  propo- 
sitions, and  indicate  the  Quality  and  Quantity  of  each  categorical 
proposition  by  the  use  of  the  letters  A,  E,  I,  and  O :  — 

(1)  Brevity  has  to  be  sought  without  sacrificing  perspicuity. 

(2)  He  that  doeth  these  things  is  like  to  a  man  that  buildeth 

his  house  upon  a  rock. 

(3)  Socrates  declared  knowledge  to  be  virtue. 

(4)  Phosphorus  does  not  dissolve  in  water. 

(5)  Nearly  all  the  troops  have  left  the  town. 

(6)  Only  ignorant  persons  hold  such  opinions. 

(7)  Few  persons  are  proof  against  temptation. 

(8)  Over  the  mountains  poured  the  barbarian  horde. 

(9)  Fine  words  butter  no  parsnips. 

(10)  Logic  is  only  common  sense  formulated. 

5.  How  does  formal  logic  interpret  the  relation  between  the 


422  Questions  and  Exercises 

subject  and  predicate  of  a  categorical  proposition  ?     Does  this 
view  do  full  justice  to  the  signification  of  propositions  ? 

6.  How  would  you  represent  by  means  of  circles  the  proposition 
'gold  is  the  most  precious  metal'  ? 

7.  What  do  you  mean  by  the  distribution  of  terms  ?  Explain 
why  negative  propositions  distribute  the  predicate,  while  affirma- 
tive propositions  do  not. 

8.  State  precisely  what  is  asserted  by  Proposition  I.  What 
forms  may  the  diagrams  which  represent  this  proposition  assume? 

Chapter  VII.  —  The  Interpretation  of  Propositions 

1.  Why  is  it  better  to  speak  of  the  Interpretation  of  proposi- 
tions than  to  use  the  term  'Immediate  Inference'? 

2.  What  is  meant  by  the  Opposition  of  propositions? 

3.  Explain  the  distinction  between  Contrary  and  Contradic- 
tory propositions. 

4.  If  proposition  O  is  false,  what  is  known  regarding  the  truth 
or  falsity  of  A,  E,  and  I? 

5.  What  is  the  simplest  proposition  which  must  be  established 
in  order  to  disprove  the  following  statements :  (a)  All  men  desire 
wealth,  (b)  No  man  is  perfectly  happy,  (c)  Some  knowledge 
is  not  of  any  value,     (d)  Pain  alone  is  evil,     (e)  All  is  not  lost. 

6.  Give  the  contrary  (or  sub-contrary),  and  the  contradictory 
of:  (a)  All  metals  are  elements,  (b)  No  coward  need  apply, 
(f)  Socrates  was  the  wisest  man  in  Athens,  (d)  Not  all  men  are 
brave,     (e)  No  man  but  a  traitor  would  have  done  this. 

7.  Give  the  Obverse  and,  in  the  cases  where  it  is  possible,  the 
Inverse,  of  the  following  propositions :  — 

(1)  All  horses  are  quadrupeds. 

(2)  Good  men  are  charitable. 

(3)  None  of  the  captives  escaped. 

(4)  Some  of  the  planets  are  not  larger  than  the  earth. 

(5)  Some  students  do  not  fail  in  anything. 


Questions  and  Exercises  423 

(6)  All  English  dukes  are  members  of  the  House  of  Lords. 

(7)  No  illogical  author  is  truly  scientific. 

8.  Convert  in  at  least  one  way:  — 

(1)  All  men  are  rational. 

(2)  Some  metals  are  readily  fusible. 

(3)  Perfect  happiness  is  impossible. 

(4)  None  of  the  captives  escaped. 

(5)  Uneasy  lies  the  head  that  wears  a  crown. 

(6)  Not  every  man  could  stand  such  hardships. 

(7)  None  but  the  brave  deserve  the  fair. 

(8)  Phosphorus  will  not  dissolve  in  alcohol. 

(9)  Hydrogen  is  the  lightest  body  known. 
(10)  The  world  is  my  idea. 

9.  Convert  by  contraposition :  — 

(1)  All  honest  men  are  of  this  opinion. 

(2)  Oxygen  can  be  prepared  by  heating  potassium  chlorate 

in  a  thin  glass  flask. 

(3)  Some  of  the  enemy  were  not  prepared  to  surrender. 

(4)  Not  all  who  came  to  scoff  remained  to  pray. 

(5)  A  triangle  is  a  plane  figure  bounded  by  three  straight 

lines. 

(6)  The  return  of  peace  had  given  fresh  confidence  to  the 

government  party. 

10.  Describe   the   logical  relation   between  each   of   the  four 
following  propositions :  — 

(1)  All  substances  which  are  material  possess  gravity. 

(2)  No  substances  which  possess  gravity  are  immaterial. 

(3)  Some  substances  which  are  immaterial  do  not  possess 

gravity. 

(4)  Some  substances  which  do  not  possess  gravity  are  im- 

material.    (Jevons.) 

11.  What  is  the  Obverse  of  the  Converse  of,  'None  of  the  planets 
shine  by  their  own  light'? 


424  Questions  and  Exercises 

12.  Can  we  logically  conclude  that  because  heat  expands  bodie^ 
therefore  cold  contracts  them?     (Jevons.) 

13.  What  is  the  logical  relation,  if  any,  between  the  two  asser- 
tions in  Proverbs  xi.  1,  'A  false  balance  is  an  abomination  to  the 
Lord;  but  a  just  weight  is  his  delight'?     (Jevons.) 

Miscellaneous  Exercises  in  Propositions 

In  the  case  of  each  of  the  single  propositions  following,  it  is 
suggested  that  the  student  first  state  it  in  strict  logical  form,  clas- 
sifying it  as  A,  E,  I,  or  O,  and  then  give,  in  the  order  named,  its 
Contrary  (or  Sub-contrary),  Contradictory,  Subaltern  (or  Superior), 
Converse,  Obverse,  and,  in  case  it  has  any,  Contrapositive  and 
Inverse. 

The  other  questions  are  self-explanatory. 

1.  Not  all  are  free  who  mock  their  bonds. 

2.  Work  that  cannot  be  paid  for  is  alone  worth  doing. 

3.  Ability  and  indolence  are  not  entirely  incompatible. 

4.  In  the  multitude  of  counsellors  there  is  wisdom. 

5.  Not  all  non-intoxicants  are  harmless.     (St.  Andrews.) 

6.  Necessity  knows  no  law. 

7.  The  meekest  of  men  may  be  incited  to  violence. 

8.  All  men  are  at  times  actuated  by  unselfish  motives. 

9.  Science  is  not  any  particular  or  chance  body  of  facts. 

10.  The  theory  of  evolution  is  not  confined  to  biology. 

1 1 .  Theologians  are  far  from  unanimity  in  their  attitude  toward 
theology. 

12.  All  lawyers  are  not  formalists. 

13.  Some  men  have  no  taste  for  literature. 

14.  Examine  the  following  argument:  — 

If  proposition  O  be  true,  I  may  be  true;  if  I  may  be  true,  A  may 
be  true:  .-.  if  O  be  true,  A  may  be  true.     (St.  Andrews.) 

15.  All  probable  events  are  possible. 


Questions  and  Exercises  425 

16.  All  parallel  lines  are  lines  which  do  not  meet. 

17.  No  one  who  is  not  a  taxpayer  can  vote  in  this  election. 

18.  What  can't  be  cured  must  be  endured. 

19.  All  bacteria  are  not  harmful. 

20.  Whatever  is,  is  right. 

21.  Some  citizens  are  not  eligible  to  the  presidential  office. 

22.  Four  years  of  study  is  required  for  a  degree. 

23.  A  point  has  no  magnitude. 

24.  Conscience  is  capable  of  becoming  more  than  the  hand- 
maid of  the  law. 

25.  Philosophy  bakes  no  bread. 

26.  Does  the  second  of  these  propositions  follow  from  the  first, 
and,  if  so,  what  is  the  logical  relation  between  them  ? 

(a)  Things  equal  to  the  same  thing  are  equal  to  each  other. 

(b)  Things  not  equal  to  each  other  are  not  equal  to  the  same 

thing. 

27.  No  wise  man  runs  into  danger  needlessly. 

28.  All  warm-blooded  animals  are  air-breathers. 

29.  Some  criminals  are  well-educated  men. 

30.  No  triangle  has  one  side  equal  to  the  sum  of  two  others. 

31.  The  line  which  bisects  the  vertical  angle  of  an  isosceles  tri- 
angle bisects  the  base. 

32.  Only  those  who  have  never  felt  a  wound  jest  at  scars. 

^^.  Assuming  that  '  All  monochromatic  light  is  coloured, '  what 
can  you  conclude  as  to  the  truth  or  falsity  of  the  following  proposi- 
tions, monochromatic  and  mixed,  and  coloured  and  white,  being  con- 
tradictories ? 

(a)  No  mixed  light  is  coloured. 

(b)  Some  coloured  light  is  not  mixed. 

(c)  All  coloured  light  is  mixed. 

(d)  Some  white  light  is  monochromatic. 

(e)  Some  mixed  light  is  not  white. 


426  Questions  and  Exercises 

34.  If 'All  who  are  happy  are  wise,'  does  it  follow  that    'An 
who  are  foolish  are  unhappy'?     (Glasgow.) 

35.  What  is  not  practicable  is  not  desirable. 

36.  Cursed  is  every  one  that  hangeth  on  a  tree. 
37    All's  well  that  ends  well. 

38.  All  cannot  receive  this  saying. 

39.  There  are  studies  much  vaunted  and  yet  of  little  utility* 

40.  All  the  men  who  do  not  row  play  ball. 

41 .  Not  to  know  me  argues  thyself  unknown. 

42.  There  is  no  folly  of  which  he  is  not  capable. 

43.  One  man  is  as  good  as  another. 

44.  If  a  man  is  not  good,  he  cannot  be  happy. 

45.  Every  man  is  not  his  own  master. 

46.  Honesty  is  not  always  the  easiest  policy. 

47.  It  is  not  possible  to  predict  events  without  knowing  their 
true  cause. 

48.  Unasked  advice  is  seldom  acceptable. 

49.  All  are  not  happy  that  seem  so. 

50.  Few  men  reason,  but  everyone  argues. 

51.  No  man  is  poor  that  does  not  think  himself  so. 

52.  Every  industrious  man  is  not  well  employed.    (St.  Andrews.) 

53.  Criticise  the  following:  — 
Granted  that  it  is  true  that, 

All  wise  men  are  mortal, 
then,      No  wise  men  are  immortal, 
and,      No  immortal  beings  are  wise  men. 
Hence  it  is  false  that, 

Some  immortal  beings  are  wise  men, 
and  that,  Some  immortal  beings  are  not  unwise  men. 
But  if  this  is  false,  it  must  be  true  that, 

All  immortal  beings  are  unwise  men, 
and  that,  Some  unwise  men  are  immortal  beings. 


Questions  and  Exercises  427 

54.  Fine  art  is  thought  suffused  with  emotion. 

55.  No  lifeless  body  has  power  to  change  its  own  state  of  motion. 

56.  No  one  is  free  who  is  enslaved  by  his  own  desires. 

57.  All  that  glitters  is  not  gold. 

58.  Few  men  of  taste  or  intelligence  are  found  among  the  very 
rich. 

59.  No  one  can  be  successful  who  is  not  both  studious  and 
ambitious. 

60.  All  the  judges  but  two  condemned  the  prisoner. 

61.  '  No  psychosis  without  neurosis;  no  neurosis  without  psy- 
chosis. '  Does  the  truth  of  the  first  half  of  this  statement  involve 
that  of  the  second? 

62.  Every  mistake  is  not  a  proof  of  ignorance. 

63.  Not  all  the  metals  are  heavier  than  water. 

64.  One  bad  general  is  better  than  two  good  ones. 

65.  In  man  there  is  nothing  great  but  mind. 

66.  Not  every  man  could  stand  such  exposure. 

67.  I  shall  not  all  die. 

68.  State  the  relation  between  the  three  propositions  contained 
in  the  following  sentence:  '  The  voluntary  muscles  are  all  striped, 
and  the  unstriped  muscles  are  all  involuntary,  but  a  few  of  the 
involuntary  muscles  are  striped. ' 

69.  'Tis  cruelty  to  load  a  falling  man. 

70.  If  it  is  true  that  there  is  'No  faith  without  works,'  does 
it  follow  that  the  doing  of  works  proves  that  faith  is  present  ? 

71.  State  the  relation  between 

(a)  Good  men  are  wise. 

(b)  Unwise  men  are  not  good. 

(c)  Some  unwise  men  are  good. 

(d)  No  good  men  are  unwise. 

72.  Philosophers  in  many  instances  do  not  avoid  mistakes. 

73.  All  who  have  nothing  in  which  to  interest  themselves  are 
unhappy. 


428  Questions  and  Exercises 

74.  You  cannot  be  just,  if  you  are  not  humane. 

75.  Few  of  us  are  not  in  some  way  infirm. 

76.  All  our  mistakes  are  not  borne  by  ourselves. 

77.  Only  the  young  prefer  bravado  to  experience. 

78.  Only  the  impartial  reason. 

79.  All  seeds  do  not  contain  albumen. 

80.  Few  candidates  were  satisfactory. 

81.  The  burnt  child  dreads  the  fire. 

82.  No  one  who  presented  himself  failed  to  pass. 

83.  Only  the  wise  are  prudent. 

84.  A  friend  in  need  is  a  friend  indeed. 

85.  Some  victories  are  worse  than  defeats. 

86.  There  is  none  virtuous,  no,  not  one. 

87.  No  one  can  be  rich  and  happy  unless  he  is  also  prudent 
and  temperate,  and  not  always  then. 

88.  No  child  ever  fails  to  be  troublesome,  if  ill-taught  and 
spoiled. 

89.  Many  a  rose  is  born  to  blush  unseen. 

90.  All  emotions  are  compound  mental  states. 

91.  It's  an  ill  wind  that  blows  good  to  nobody. 

92.  Some  laws  arise  from  custom. 

93.  Not  all  who  are  called  are  chosen. 

94.  He  envies  others'  wealth  who  has  none  himself. 

95.  Only  doctors  understand  this  subject. 

96.  If  it  is  true  that  'Students  who  do  their  work  faithfully 
should  receive  university  credit,'  does  it  follow  that  'Students 
should  receive  university  credit  for  a  faithful  effort  to  do  their 
work '  ? 

97.  A  few  Greeks  vanquished  the  vast  army  of  Darius. 

98.  Only  ignorant  persons  hold  such  opinions. 

99.  If  it  is  true  that  'There  is  no  disgrace  in  losing  when  one 
has  done  one's  best,'  does  it  follow  that  'Those  who  win  deserve 
no  particular  glory'  ? 


Questions  and  Exercises  429 

100.  If  certain  admirable  qualities,  such  as  concentration,  the 
capacity  for  hard  work,  and  persistence,  will  carry  a  man  no 
farther  than  tenth  in  his  class,  does  it  follow  that  the  first  nine 
places  can  be  won  only  by  men  without  concentration,  persistence, 
or  the  capacity  for  hard  work?     (N.Y.  Evening  Post.) 

101.  Since  'Hottentots  are  men,'  can  we  say  that  a  clever 
Hottentot  is  a  clever  man? 

102.  In  the  case  of  the  proposition  'All  wise  acts  are  honest 
acts,'  answer  the  following  questions:  (a)  How  is  its  converse 
related  to  its  subaltern?  (b)  How  is  its  converse  related  to  the 
converse  of  its  subaltern?  (c)  How  is  its  subaltern  related  to 
its  contradictory?     (Jevons.) 

103.  Name  the  logical  process  by  which  we  pass  from  each  of 
the  following  propositions  to  the  succeeding  one:  — 

(a)  All  metals  are  elements. 

(b)  No  metals  are  non-elements. 

(c)  No  non-elements  are  metals. 

(d)  All  non-elements  are  non-metals. 

(e)  All  metals  are  elements. 
(J)  Some  elements  are  metals. 

(g)  Some  metals  are  elements.     (Jevons.) 

104.  None  but  a  logical  author  is  a  truly  scientific  author. 

Chapter  VIII.  —  The  Syllogism  and  its  Rules 

1.  What  is  the  relation  of   the  Proposition  and  the  Syllogism? 

2.  What  is  the  function  of    the  Middle  Term  in  a  Syllogism? 

3.  How  are  the  major  and  minor  terms,  and  the  major  and 
minor  premises  of  a  Syllogism  distinguished  ? 

4.  Prove  the  seventh  and  eighth  canon  of  the  Syllogism,  (a)  by 
means  of  the  previous  rules,  and  (b)  by  the  use  of  circles. 

5.  Construct  an  argument  to  illustrate  the  fallacy  of  ambigu- 
ous middle  term. 

6.  Arrange   the    following   arguments    in    the   regular   logical 


430  Questions  and  Exercises 

order  of  major  premise,  minor  premise,  and  conclusion,  and 
examine  them  to  see  whether  they  conform  to  the  canons  of  the 
Syllogism :  — 

(i)  Gold  is  not  a  compound  substance;   for  it  is  a  metal, 
and  none  of  the  metals  are  compounds. 

(2)  All  national  holidays  are  bank  holidays,  the  bank  will 

therefore  be  closed  on  the  Fourth  of  July. 

(3)  All  cruel  men  are  cowards,  no  college  men  are  cruel, 

therefore  no  college  men  are  cowards. 

(4)  Some  useful  metals  are  becoming  rarer.     Iron  is  a  useful 

metal,  and  is  therefore  becoming  rarer. 

(5)  This  man  shares  his  money  with   the  poor,  but  no  thief 

ever  does  this,  therefore  this  man  is  not  a  thief. 

(6)  He  who  is  content  with  what  he  has  is  truly  rich.     An 

envious  man  is  not  content  with  what  he  has;  no  en- 
vious man  therefore  is  truly  rich. 
7.  What  does  the  Figure  of  an  Argument  depend  upon?     How 
do  you  distinguish  the  four  figures? 

Chapter  IX.  —  The  Valid  Moods  and  the  Reduction  of  Figures 

1.  Arrange  the  following  arguments  in  logical  order,  and  give 
the  mood  and  figure  in  each  case :  — 

(1)  No  P  is  M,  (2)  All  M  is  S, 

Some  S  is  M,  Some  M  is  P, 

Therefore  some  S  is  not  P.  Therefore  some  S  is  P. 

2.  Name  the  premises  from  which  valid  conclusions  may  be 
drawn,  no  account  being  taken  of  figures :  — 

AA,      EO,      IA,      10,       II,     EE,      EI,      AE,     EA,      00. 

3.  Prove  the  special  canons  of  the  fourth  figure. 

4.  'The  middle  term  must  be  distributed  once  at  least.'  In 
what  figures  may  it  be  distributed  twice?  What  is  the  character 
of  the  conclusion  when  this  occurs? 


Questions  and  Exercises  43 1 

5.  Prove  generally  that  when  the  major  term  is  predicate  in  its 
premise,  the  minor  premise  must  be  affirmative. 

6.  If  the  major  term  be  distributed  in  its  premise,  but  used  undis- 
tributively  in  the  conclusion,  determine  the  mood  and  figure. 

7.  Explain  why  we  can  obtain  only  negative  conclusions  by 
means  of  the  second  figure  and  particular  conclusions  by  means  of 
the  third  figure. 

8.  What  conclusions  do  AA,  AE,  and  EA,  yield  in  the  fourth 
figure  ?     Explain. 

9.  Is  it  possible  for  both  major  and  minor  terms  to  be  undis- 
tributed at  the  same  time  in  the  premises?  If  so,  construct  an 
argument  where  this  is  the  case. 

10.  What  do  you  understand  by  Reduction?  Reduce  the 
following  argument  to  the  first  figure:  — 

No  fixed  stars  are  planets, 

All  planets  are  bright  and  shining, 

Therefore  some  bright  and  shining  bodies  are  not  fixed  stars. 

Chapter   X.  —  Abbreviated  and  Irregular  Arguments 

1.  Complete  the  following  arguments,  determine  their  mood 
and  figure,  and  examine  them  to  see  if  they  violate  any  of  the  rules 
of  the  syllogism :  — 

(1)  Blessed  are  the  meek,  for  they  shall  inherit  the  earth. 

(2)  He  must  be  a  strong  man ;  for  he  was  on  the  crew. 

(3)  Zoophytes  have  no  flowers ;  therefore  they  are  not  plants. 

(4)  None  but  material  bodies  gravitate;  therefore  air  is  a 

material   body. 

(5)  He  has  been  a  politician  for  years,  and  is  therefore  not 

to  be  trusted. 

2.  Illustrate  the  difference  between  the  Progressive  or  Synthetic, 
and  the  Regressive  or  Analytic,  methods  as  employed  in  Mathematics 
and  Pyschology.  May  a  science  employ  both  methods  at  the  same 
time? 


432  Questions  and  Exercises 

3.  Break  up  the  concrete  examples  of  Sorites  given  on  pages  136, 
137,  into  syllogisms. 

4.  Show  generally  why  all  the  premises  except  the  first  in  the 
Aristotelian  Sorites  must  be  universal. 

5.  Prove  that  in  the  Goclenian  Sorites  the  first  premise  alone 
can  be  negative,  and  the  last  alone  particular. 

6.  In  the  examples  of  arguments  given  on  page  139,  is  there 
any  middle  term?  If  not,  what  serves  as  the  standard  of  com- 
parison ? 

7.  What  is  the  general  principle  on  which  all  a  fortiori  arguments 
proceed  ?     How  can  you  tell  when  an  argument  is  of  this  type  ? 

8.  State  the  argument  implied  in  the  following:  — 

'  If  a  man  love  not  his  brother  whom  he  hath  seen,  how  shall 
he  love  God  whom  he  hath  not  seen?' 


Chapter   XI.  —  Hypothetical  and  Disjunctive  Arguments 

1.  What  reasons  are  there  for  classifying  the  disjunctive  propo- 
sition as  conditional  ? 

2.  What  are  the  rules  of  the  hypothetical  syllogism? 

3.  Is  it  ever  possible  to  obtain  a  valid  conclusion  by  denying 
the  antecedent  or  affirming  the  consequent? 

4.  Determine  which  of  the  following  hypothetical  arguments  are 
valid  and  which  invalid ;  then  express  the  latter  in  the  categorical 
form  pointing  out  what  are  the  categorical  fallacies  which  result : — ■ 

(1)  If  a  man  is  avaricious,  he  will  be  unhappy;    but  A  is 

unhappy,  and  we  may  therefore  conclude  that  he  is 
avaricious. 

(2)  If  A  is  B,  C  is  D;  but  A  is  B,  therefore  we  may  conclude 

that  C  is  D. 

(3)  If  the  door  were  locked,  the  horse  would  not  be  stolen ; 

but  the  horse  is  not  stolen,  therefore  the  door  must 
have  been  locked. 


Questions  and  Exercises  433 

(4)  If  man  were  not  capable  of  progress,  he  would  not  differ 

from  the  brutes;  but  man  does  differ  from  the  brutes, 
therefore  he  is  capable  of  progress. 

(5)  If  he  had  studied  his  lesson,  he  would  have  been  able  to 

recite;    but  he  was  able  to  recite,  and  therefore  must 
have  studied  his  lesson. 

(6)  If  it  becomes  colder  to-night,  the  pond  will  be  frozen  over; 

but  it  will  not  become  colder  to-night,  therefore  the 
pond  will  not  be  frozen  over. 

5.  What  aspects  of  thinking  are  emphasized  by  the  categorical 
and  hypothetical  forms  of  reasoning  respectively  ? 

6.  How  far  may  the  disjunctive  proposition  be  regarded  as 
an  expression  of  ignorance,  and  what  is  the  justification  for  the 
statement  that  it  involves  systematic  knowledge? 

7.  To  what  fallacy  is  the  disjunctive  argument  specially  liable? 

8.  How  would  you  criticise  the  dilemmatic  arguments  given  on 
page  158? 

9.  State  the  following  fully  as  a  dilemma :  — 

'There  are  two  kinds  of  things  which  we  ought  not  to  fret  about; 
what  we  can  help,  and  what  we  cannot. '     ( Whately.) 

10.  '  When  men  are  pure,  laws  are  useless ;  when  men  are  cor- 
rupt, laws  are  broken.'     (Jevons.) 

State  the  above  fully  as  a  dilemma,  and  construct  a  counter- 
dilemma  in  rebuttal. 

Chapter   XII. —  Fallacies  of  Deductive  Reasoning 

1.  What  is  the  distinction  between  errors  of  interpretation  and 
fallacies  in  reasoning? 

2.  Why  is  the  detection  of  material  fallacies  a  proper  subject 
of  logic  ? 

3.  If  it  is  true  that  'all  the  righteous  people  are  happy,'  can 
we  conclude  that  '  all  unhappy  people  are  unrighteous  '  ?  If  so, 
how  do  we  pass  from  the  first  statement  to  the  second  ? 

2F 


434  Questions  and  Exercises 

4.  Can  we  proceed  logically  from  the  proposition,  'all  good 
citizens  vote  at  elections/  to  'all  who  vote  at  elections  are  good 
citizens'? 

5.  Does  the  statement  that  'some  sciences  are  useful,'  justify 
the  proposition  that  'some  useful  things  are  not  sciences'? 

6.  Mention  the  fallacies  of  Equivocation,  and  explain  what  is 
common  to  them  all. 

7.  Explain  the  terms:  Petitio  Principii,  Cir cuius  in  probando, 
Argumentum  ad  hominem,  Argumentum  ad  populum. 

8.  Examine  the  following  reasoning:  'The  argument  from 
design  must  be  regarded  as  without  value;  for  it  has  been  re- 
jected by  Spinoza,  Kant,  Spencer,  and  Darwin.' 

9.  Point  out  and  name  the  fallacy  or  fallacies  in  the  following :  — 

(1)  We  know  that  God  exists  because  the  Bible  tells  us  so; 

and  we  know  that  whatever  the  Bible  affirms  must  be 
true,  because  it  is  of  Divine  origin.     (Edinburgh.) 

(2)  This  is  a   dangerous   doctrine,  for  we  find   it   upheld 

by    men  who    avow    their    disbelief  in   Revelation. 
(Jevons.) 

(3)  He  must  be  a  Mahometan,  for  all  Mahometans  hold 

these  opinions.     (Edinburgh.) 

(4)  It  is  not  right  for  you  to  devote  all  your  time  to  archae- 

ological research,  for  if  all  men  did  so,  the  business 
of  the  world  could  not  go  on.     (Boyce  Gibson.) 

(5)  Every  incident  in  this  man's  account  of  the  affair  is 

natural  and  probable,  and  we  may  therefore  regard 
his  story  as  quite  possibly  true.     (Jevons,  modified.) 

(6)  Great  men  have  been  derided,  and  I  am  derided;    which 

proves   that   my   theory  ought  to  be  adopted.     (De 
Morgan.) 


Questions  and  Exercises  435 

Miscellaneous  Examples  of  Deductive  Arguments 

Arrange  the  following  arguments  whenever  possible  in  regular 
logical  order,  supplying  premise  or  conclusion  where  either  is 
lacking,  or  condensing  when  several  sentences  are  used  to  state 
one  proposition;  determine  whether  or  not  the  arguments  are 
valid;  give  the  mood  and  figure  of  the  valid  categorical  argu- 
ments ;  if  any  argument  is  invalid,  point  out  and  name  the  fallacy 
involved :  — 

1.  All  virtue  is  praiseworthy,  and  charity  is  a  virtue;  therefore 
charity  is  praiseworthy. 

2.  All  colours  are  physical  phenomena;  but  no  sound  is  a 
colour,  therefore  no  sound  is  a  physical  phenomenon. 

3.  Some  minerals  are  precious  stones,  all  topazes  are  precious 
stones;  therefore  some  minerals  are  topazes. 

4.  Some  acts  of  homicide  are  laudable;  therefore  some  cruel 
things  are  laudable. 

5.  If  he  has  found  the  treasure,  he  is  rich ;  but  he  has  not  found 
it;  therefore  he  is  not  rich. 

6.  He  must  be  a  Democrat;  for  all  the  Democrats  believe  in 
Free  Trade. 

7.  The  receiver  of  stolen  property  should  be  punished;  you 
have  received  stolen  property,  and  should  therefore  be  punished. 
(Glasgow.) 

8.  Whoever  believes  this  is  a  heretic ;  so  that  you  are  no  heretic, 
for  you  do  not  believe  this.     (Glasgow.) 

9.  Good  men  write  good  books;  this  is  a  good  book,  and  there- 
fore its  writer  was  a  good  man.     (Glasgow.) 

10.  No  man  desires  pain,  and  without  pain  your  friend's 
cure  is  impossible;  therefore  he  will  not  desire  to  be  cured 
(Glasgow.) 


436  Questions  and  Exercises 

ii.  Nothing  real  is  irrational.  Everything  unreal  is  transitory. 
Therefore  all  irrational  things  are  transitory.     (St.  Andrews.) 

12.  Language  is  the  communication  of  information  by  signs, 
and  so  we  must  say  that  the  wagging  of  a  dog's  tail  is  language. 
(St.  Andrews.) 

13.  If  only  the  ignorant  despise  knowledge,  this  man  cannot 
be  ignorant,  for  he  praises  it.     (Edinburgh.) 

14.  Whatever  is  given  on  the  evidence  of  sense  may  be  taken 
as  a  fact;  the  existence  of  God,  therefore,  is  not  a  fact,  for  it  is 
not  evident  to  sense.     (St.  Andrews.) 

15.  This  explosion  must  have  been  occasioned  by  gunpowder; 
for  nothing  else  would  have  possessed  sufficient  force. 

16.  This  burglary  is  the  work  of  a  professional;  for  an  amateur 
would  not  have  been  half  so  clever. 

17.  No  stupid  person  can  become  President  of  the  United 
States;  therefore  Mr.  Cleveland  and  Mr.  McKinley  must  both 
have  been  men  of  ability. 

18.  Since  almost  all  the  organs  of  the  body  have  some  use, 
the  vermiform  appendix  must  be  useful. 

19.  Every  candid  man  acknowledges  merit  in  a  rival,  every 
learned  man  does  not  do  so;  therefore  learned  men  are  not 
candid. 

20.  Every  book  is  liable  to  error,  every  book  is  a  human  pro- 
duction, therefore  all  human  productions  are  liable  to  error. 

2i.  Learned  men  sometimes  become  mad;  but,  as  he  is  not 
learned,  there  is  no  danger  of  his  sanity. 

22.  If  this  candidate  used  money  to  secure  his  election,  he 
deserved  defeat ;  but  he  did  not  use  money  in  this  way,  and  there- 
fore did  not  deserve  defeat. 

23.  All  valid  syllogisms  have  three  terms;  this  syllogism  is 
therefore  valid,  for  it  has  three  terms. 


Questions  and  Exercises  437 

24.  No  persons  destitute  of  imagination  are  true  poets ;  some 
persons  destitute  of  imagination  are  good  reasoners;  therefore 
some  good  reasoners  are  not  true  poets. 

25.  Only  material  bodies  gravitate;    ether  does  not  gravitate. 

26.  In  reply  to  the  gentleman's  arguments,  I  need  only  say 
that  two  years  ago  he  advocated  the  very  measure  which  he  now 
opposes. 

27.  Haste  makes  waste,  and  waste  makes  want;  therefore 
a  man  never  loses  by  delay.     (Glasgow.) 

28.  C  is  not  D,  for  A  is  B;  and  I  know  that  whenever  A  is 
not  B,  C  is  D.     (Glasgow.) 

30.  The  existence  of  sensations  consists  in  being  perceived; 
all  objects  are  really  collections  of  sensations;  therefore,  their 
existence  consists  in  being  perceived.     (Glasgow.) 

31.  None  but  utilitarians  are  hedonists;  practical  men  are 
utilitarians;   therefore   they   are   hedonists.     (Glasgow.) 

32.  If  he  claims  that  he  did  not  steal  the  goods,  why,  I  ask 
did  he  hide  them,  as  no  thief  ever  fails  to  do  ? 

t,^.  If  this  therefore  be  absurd  in  fact  and  theory,  it  must  also 
be  absurd  in  idea,  since  nothing  of  which  we  can  form  a  clear 
and  distinct  idea  is  impossible.  (Hume,  Treatise  of  Human 
Nature.) 

34.  Whatever  is  produced  without  a  cause  is  produced  by 
nothing,  or  in  other  words  has  nothing  for  its  cause.  But  nothing 
can  never  be  a  cause.  Hence  every  object  has  a  real  cause  of 
its  existence.     (Hume,  Treatise.) 

35.  Everything  must  have  a  cause;  for  if  anything  wanted 
a  cause  it  would  produce  itself,  that  is,  exist  before  it  existed, 
which  is  impossible.     (Hume,  Treatise). 

36.  If  it  be  true,  as  Mr.  Spencer  thinks,  that  the  past  expe- 
rience of  the  race  has  produced  innate  ideas  and  feelings,  Weis- 
mann's  denial  of  Use-inheritance  would  be  refuted.  Certainly, 
but  it  is  just  possible  that  Mr.  Spencer's  theory  is  not  true. 


438  Questions  and  Exercises 

37.  Democracy  is  not  a  perfect  form  of  government,  for  undei 
it  there  are  able  men  who  do  not  get  power;  and  so  it  allows 
men  to  get  power  who  are  not  able. 

38.  Of  university  professors,  some  are  zealous  investigators, 
and  some  good  teachers.  A  is  an  excellent  teacher,  and  we 
may  therefore  conclude  that  he  is  not  a  zealous  investigator. 

39.  Seeing  that  abundance  of  work  is  a  sure  sign  of  industrial 
prosperity,  it  follows  that  fire  and  hurricane  benefit  industry, 
because  they  undoubtedly  create  work.       (St.  Andrews.) 

40.  I  will  have  no  more  doctors;  I  see  that  all  of  those  who 
have  died  this  winter  have  had  doctors.     (St.  Andrews.) 

41.  If  a  man  is  educated,  he  does  not  want  to  work  with 
his  hands;  consequently,  if  education  is  universal,  industry  will 
cease.     (London.) 

42.  Show  why  IE  is  an  impossible  mood  in  all  the  figures  of  the 
syllogism,  while  EI  is  possible  in  all  of  them.     (Glasgow.) 

43.  If  acquired  variations  are  transmitted,  there  must  be  some 
unknown  principle  of  heredity;  if  they  are  not  transmitted,  there 
must  be  some  unknown  factor  of  evolution.     (Osborn.) 

44.  Some  plant-products  harmful  to  insects  are  not  a  pro- 
tective development;  for  all  tannin  is  harmful  to  insects, 
and  most  certainly  not  all  tannin  is  a  protective  development. 
(St.  Andrews.) 

45.  Art  is  not  fostered  by  money;  for  a  true  artist  would  practise 
his  art  for  its  own  sake,  and  a  bad  artist  should  not  be  encouraged. 
(St.   Andrews.) 

46.  The  spectra  of  compound  bodies  become  less  complex  with 
heat;  but  the  spectra  of  the  elements  do  not,  since  they  are  not  the 
spectra  of  compound  bodies.     (St.  Andrews.) 

47.  What  can  you  tell  about  a  valid  syllogism  if  you  know:  — 
(1)  that  only  the  middle  term  is  distributed;   (2)  that  only  the 


Questions  and  Exercises  439 

middle  and  minor  terms  are  distributed;   (3)  that  all  three  terms 
are  distributed?     (Glasgow). 

48.  None  but  the  wise  are  good,  and  none  but  the  good  are 
happy;  therefore  none  but  the  wise  are  happy.     (Edinburgh.) 

49.  Giving  advice  is  useless.  For  either  you  advise  a  man 
what  he  means  to  do,  in  which  case  the  advice  is  superfluous;  or 
you  advise  him  what  he  does  not  mean  to  do,  and  the  advice  is 
ineffectual.     (London.) 

50.  No  pauper  has  a  vote;  AB  is  not  a  pauper,  therefore  he 
has  a  vote.     (St.  Andrews.) 

51.  The  love  of  nature  is  never  found  either  in  the  stupid  or  the 
immoral  man,  therefore  stupidity  and  virtue  are  incompatible. 
(Edinburgh.) 

52.  Not  all  educated  persons  spell  correctly;  for  one  often  finds 
mistakes  in  the  papers  of  University  students. 

53.  Free  Trade  is  a  great  boon  to  the  workingman;  for  it 
increases  trade,  and  this  cheapens  articles  of  ordinary  consumption ; 
this  gives  a  greater  purchasing  power  to  money,  which  is  equiva- 
lent to  a  rise  in  real  wages,  and  any  rise  in  real  wages  is  a  boon  to 
the  workingman. 

54.  The  figure  of  Tell  cannot  be  historic,  else  he  must  have  been 
mentioned  by  early  historians,  or  his  personality  would  be  necessary 
to  explain  known  facts  of  history.     (St.  Andrews.) 

55.  Nerve  power  does  not  seem  to  be  identical  with  electricity; 
for  it  is  found  that  when  a  nerve  is  tightly  compressed  nervous 
action  does  not  go  on,  but  electricity  can  nevertheless  pass. 
(Jevons.) 

56.  Carbon,  which  is  one  of  the  main  sources  of  the  nourishment 
of  plants,  cannot  be  dissolved  in  water  in  its  simple  form,  and  can- 
not therefore  be  absorbed  in  that  form  by  plants,  since  the  cells 
absorb  only  dissolved  substances.  All  the  carbon  found  in  plants 
must  consequently  have  entered  them  in  a  form  soluble  in  water, 
and  this  we  find  in  carbonic  acid.     (Adamson,  Jevons.) 


440  Q?(estions  and  Exercises 

57.  No  punishment  should  be  allowed  for  the  sake  of  the  good 
that  may  come  of  it;  for  all  punishment  is  an  evil,  and  we  are  not 
justified  in  doing  evil  that  good  may  come  of  it.     (Edinburgh.) 

58.  Prove  that  when  the  minor  term  is  predicate  in  the  minor 
premise  of  a  syllogism,  the  conclusion  cannot  be  A.     (Glasgow.) 

59.  We  must  be  guided  by  the  decisions  of  our  ancestors,  for 
old  age  is  wiser  than  youth.     (Oxford.) 

60.  If  education  is  popular,  compulsion  is  unnecessary;  if 
unpopular,  compulsion  will  not  be  tolerated.     (Oxford.) 

61.  Wealth  is  in  proportion  to  value,  value  to  efforts,  efforts 
to  obstacles;  therefore  wealth  is  in  proportion  to  obstacles. 
(Jevons.) 

62.  If  the  train  is  late,  I  shall  miss  my  appointment;  if  it  is 
not  late,  I  shall  not  reach  the  depot  in  time  to  go  by  it ;  therefore, 
in  any  case,  I  shall  miss  my  appointment. 

63.  He  who  spareth  the  rod  hateth  his  child;  the  parent  who 
loves  his  child  therefore  spareth  not  the  rod. 

64.  Whatever  tends  to  withdraw  the  mind  from  pursuits  of  a 
low  nature  deserves  to  be  promoted;  classical  learning  does  this, 
since  it  gives  us  a  taste  for  intellectual  enjoyments;  therefore  it 
deserves  to  be  promoted. 

65.  As  against  the  proposition  that  the  formation  of  public 
libraries  prevents  private  individuals  from  purchasing,  and  so  de- 
creases the  sale  of  books,  a  writer  urges  that  whatever  encourages 
the  reading  of  books  encourages  the  buying  of  books.  It  is  a 
library's  purpose  to  encourage  reading,  and  hence  the  net  result 
is  rather  to  increase  than  to  lessen  purchases. 

66.  The  express  train  alone  does  not  stop  at  this  station,  and, 
as  the  last  train  did  not  stop,  it  must  have  been  the  express  train. 
(Glasgow.) 

67.  The  infliction  of  pain  is  sometimes  justifiable;  for  a  just 
punishment  always  involves  pain.     (Glasgow.) 


Questions  and  Exercises  441 

68.  "The  truth  is,  that  luxury  produces  much  good.  A  man 
gives  half  a  guinea  for  a  dish  of  green  peas;  how  much  gardening 
does  this  occasion  ?"     (Dr.  Johnson.) 

69.  Protective  duties  should  be  abolished;  for  they  are  injurious 
if  they  produce  scarcity,  and  they  are  useless  if  they  do  not.  (Ox- 
ford.) 

70.  Animals  only  are  sentient  beings;  all  plants  are  insentient. 
(St.  Andrews.) 

71.  Only  native-born  citizens  are  eligible  to  this  office;  but  as 
you  have  this  qualification,  you  need  not  hesitate  to  run  for  it. 
(St.  Andrews.) 

72.  A  primary  election  law  is  necessary,  for  at  present  the 
people  have  no  voice  in  the  nomination  of  candidates  for  office. 

73.  I  do  not  see  how  Mr.  Rhodes  can  escape  censure.  If  he 
knew  of  Dr.  Jameson's  raid,  he  was  guilty  of  complicity;  if  he 
did  not,  of  negligence.     (St.  Andrews.) 

74.  Business  enterprises  are  most  successful  when  managed  by 
those  who  have  a  direct  interest  in  them;  therefore  enterprises 
carried  on  by  the  State  are  not  likely  to  succeed. 

75.  All  P  is  M;  All  S  is  M;  therefore  Some  not-S  is  not-P. 
(Glasgow.) 

76.  Wherever  ideas  have  become  indissolubly  associated,  it  is 
beyond  our  power  to  represent  them  separately;  our  attitude  is 
that  of  belief.  Belief  then  may  be  defined  as  the  consequence  of 
an  indissoluble  association  of  ideas.     (Glasgow.) 

77.  No  reason,  however,  can  be  given  why  the  general  happiness 
is  desirable,  except  that  each  person,  so  far  as  he  believes  it  to  be 
attainable,  desires  his  own  happiness.  This,  however,  being  a 
fact,  we  have  not  only  all  the  proof  which  the  case  admits  of,  but 
all  which  it  is  possible  to  require,  that  happiness  is  a  good,  that 
each  person's  happiness  is  a  good  to  that  person,  and  the  gen- 
eral happiness,  therefore,  a  good  to  the  aggregate  of  all  persons. 
(Mill's  Utilitarianism?) 


442  Questions  and  Exercises 

78.  This  man  is  a  Protestant;  for  he  exercises  the  right  or 
private  judgment. 

79.  If  the  orbit  of  a  comet  is  diminished,  either  the  comet  passes 
through  a  resisting  medium,  or  the  law  of  gravitation  is  partially 
suspended.  But  the  second  alternative  is  inadmissible.  Hence 
if  the  orbit  of  a  comet  is  diminished,  there  is  present  a  resisting 
medium. 

80.  How  do  we  know  that  our  intuitive  beliefs  concerning  the 
world  are  invariably  true?  Either  it  must  be  from  experience 
establishing  the  harmony,  or  an  intuitive  belief  must  certify  the 
correctness.  Now  experience  cannot  warrant  such  harmony 
except  in  so  far  as  it  has  been  perceived.  Still  more  futile  is  it  to 
make  one  instinctive  belief  the  cause  of  another.  Thus  we  cannot 
know  that  any  intuitive  belief  is  universally  valid.     (Bain.) 

81.  Which  of  the  following  are  real  inferences  ?  (1)  'This  weighs 
that  down,  therefore  it  is  heavier';  (2)  'This  piece  of  marble  is 
larger  than  that,  and  therefore  is  heavier.' 

82.  The  parts  of  pure  space  are  immovable,  which  follows 
from  their  inseparability,  motion  being  nothing  but  change  of 
distance  between  any  two  things;  but  this  cannot  be  between 
parts  that  are  inseparable,  which  therefore  must  be  at  perpetual 
rest  one  amongst  another. 

83.  All  civilized  peoples  are  progressive;  all  uncivilized  peoples 
are  superstitious;  therefore  some  superstitious  peoples  are  not 
progressive.     (St.  Andrews.) 

84.  Ignorance  is  no  crime ;  and  as  you  did  not  know  what  you 
were  doing,  you  should  not  be  punished.     (St.  Andrews.) 

85.  He  could  not  face  bullets  on  the  field  of  battle,  and  is  there- 
fore a  coward.     (St.  Andrews.) 

86.  If  a  man  be  rightfully  entitled  to  the  produce  of  his  labour, 
then  no  one  can  be  rightfully  entitled  to  anything  which  is  not  the 
produce  of  his  labour.     (St.  Andrews.) 


Questions  and  Exercises  443 

87.  In  moral  matters  we  cannot  stand  still;  therefore  he  who 
does  not  go  forward  is  sure  to  fall  behind.     (Glasgow.) 

88.  A  man  that  hath  no  virtue  in  himself  ever  envieth  virtue  in 
others;  for  men's  minds  will  either  feed  upon  their  own  good  or 
upon  others'  evil ;  and  who  wanteth  the  one  will  prey  upon  the 
other.     (Glasgow.) 

89.  A  successful  author  must  be  either  very  industrious  or  very 
talented:  Gibbon  was  very  industrious,  therefore  he  was  not  very 
talented.     (Glasgow.) 

90.  He  who  calls  you  a  man  speaks  truly;  he  who  calls  you  a 
fool  calls  you  a  man;  therefore  he  who  calls  you  a  fool  speaks 
truly.     (Glasgow.) 

91.  If  a  body  moves,  it  must  move  either  in  the  place  where  it  is, 
or  in  the  place  where  it  is  not.  But  a  body  cannot  move  in  the 
place  where  it  is,  nor  yet  in  the  place  where  it  is  not.  Hence  a 
body  cannot  move  at  all. 

92.  We  have  no  perfect  idea  of  anything  but  a  perception.  A 
substance  is  entirely  different  from  a  perception.  We  have  there- 
fore no  idea  of  substance.     (Hume.) 

93.  Every  good  government  promotes  the  intelligence  of  the 
people,  and  no  desp^ism  does  that.     (Bain.) 

94.  He  was  too  impulsive  a  man  not  to  have  committed  many 
errors.     (Bain.) 

95.  A  true  philosopher  is  independent  of  the  caprices  of  fortune, 
for  he  places  his  chief  happiness  in  moral  and  intellectual  excellence. 

96.  Educated  among  savages,  he  could  not  be  expected  to  know 
the  customs  of  polite  society.     (Bain.) 

97.  No  war  is  long  popular;  for  every  war  increases  taxation, 
and  the  popularity  of  anything  that  touches  our  pockets  is  very 
short-lived. 

98.  There  can  be  no  such  thing  as  an  omniscient  mind,  since  all 
thinking  is  a  succession  of  mental  states.     (St.  Andrews.) 


444  Questions  and  Exercises 

99.  Morality  is  either  superfluous  or  unavailing,  according  as  the 
universe  is  righteous  or  not.     (St.  Andrews.) 

100.  The  earth's  position  must  be  fixed,  if  the  fixed  stars  are 
seen  at  all  times  in  the  same  situations;  now  the  fixed  stars  are 
not  seen  at  all  times  in  the  same  situations;  therefore  the  earth's 
position  is  not  fixed.     (Edinburgh.) 

101.  The  table  we  see  seems  to  diminish  as  we  move  from  it; 
but  the  real  table  suffers  no  change;  it  was  not,  therefore,  the 
table  itself,  but  only  its  image,  that  was  present  to  the  mind. 
(Jevons.) 

102.  The  general  object  which  all  laws  have,  or  ought  to  have,  in 
common,  is  to  augment  the  total  happiness  of  the  community; 
and  therefore,  in  the  first  place,  to  exclude  as  far  as  may  be  every- 
thing that  tends  to  subtract  from  that  happiness :  in  other  words, 
to  exclude  mischief.  But  all  punishment  is  mischief;  all  punish- 
ment in  itself  is  evil.  Upon  the  principle  of  utility,  if  it  ought  at 
all  to  be  admitted,  it  ought  only  to  be  admitted  in  as  far  as  it  prom- 
ises to  exclude  some  greater  evil.     (Bentham.) 

103.  Experiments  for  the  purpose  of  ascertaining  the  functions 
of  the  various  organs  in  animals  cause  pain,  and  as  we  are  not  war- 
ranted in  causing  pain  to  any  sentient  creature,  such  experiments 
are  wrong. 

104.  Thou  shalt  not  bear  false  witness  against  thy  neighbour. 

105.  It  is  injustice  to  the  intellect  of  women  to  refuse  them  the 
suffrage ;  for  the  reigns  of  many  queens  have  been  famous  for 
literary  productions.     (Oxford.) 

106.  The  two  propositions,  'Aristotle  is  dead,'  and  'Aristotle  is 
living,'  are  both  intelligible  propositions;  they  are  both  of  them  true 
or  both  of  them  false,  because  all  intelligible  propositions  must  be 
either  true  or  false.     (Edinburgh.) 

107.  He  is  innocent,  for  he  has  faced  his  accusers;  a  guilty  man 
would  run  away.     (Hyslop.) 


Questions  and  Exercises  445 

108.  All  civilized  people  are  inhabitants  of  the  temperate  zones. 
Few  Indians  are  civilized,  and  therefore  few  Indians  are  inhabitants 
of  the  temperate  zones.     (Hyslop.) 

109.  In  what  are  called  our  free  actions  we  are  either  undeter- 
mined by  motives,  in  which  case  we  act  from  pure  caprice,  or  we 
are  determined  by  motives,  in  which  case  our  freedom  has  no  real 
existence.     (St.  Andrews.) 

1 10.  If  a  nation  wants  Protection,  it  is  not  prosperous  under  Free 
Trade,  as  England  must  be,  since  it  does  not  want  Protection. 
(St.  Andrews.) 

in.  Either  all  the  facts  of  the  major  premise  of  any  syllogism 
have  been  examined,  or  some  of  them  have  not ;  therefore  the 
syllogism  is  either  useless  or  fallacious.     (St.  Andrews.) 

112.  Few  treatises  of  science  convey  important  truths  without 
intermixture  of  error,  in  a  perspicuous  and  interesting  form ;  and 
therefore,  though  a  treatise  would  deserve  much  attention  which 
should  possess  such  excellence,  it  is  plain  that  few  treatises  of 
science  deserve  much  attention.     (Whately.) 

113.  All  aristocracies  are  self-willed ;  some  self-willed  people  are 
not  cruel;  therefore  some  aristocracies  are  not  cruel. 

114.  Some  men  of  inferior  ability  are  legislators.  All  peers  are 
legislators.     Therefore  some  peers  are  men  of  inferior  ability. 

115.  All  able  men  are  consistent  with  themselves;  he  who 
changes  his  opinions  is  not  consistent  with  himself;  therefore  he 
who  changes  his  opinions  is  not  an  able  man. 

116.  To  allow  every  man  an  unbounded  freedom  of  speech 
must  always  be,  on  the  whole,  advantageous  to  the  state ;  for  it  is 
highly  conducive  to  the  interests  of  the  community  that  each 
individual  should  enjoy  a  liberty  perfectly  unlimited  of  express- 
ing his  sentiments.     (Whately.) 

117.  He  who  necessarily  lies  or  tells  the  truth  is  not  a  free 
agent;  but  you  must  necessarily  lie  or  tell  the  truth;  therefore 
you  are  not  a  free  agent.     (Whately.) 


446  Questions  and  Exercises 

118.  It  is  no  uncommon  occurrence  to  gain  a  high  prize  in  the 
lottery;  and  what  is  no  uncommon  occurrence  may  reasonably 
be  expected;  therefore  I  may  reasonably  expect  to  gain  a  high 
prize  on  my  ticket.     (Whately.) 

119.  If  genius  were  normal,  it  would  be  good  and  worthy  of 
cultivation,  but  being  abnormal,  it  is  not.     (St.  Andrews.) 

120.  If  truthfulness  is  never  found  save  with  scrupulousness, 
and  if  truthfulness  is  incompatible  with  stupidity,  it  follows  that 
stupidity  and  scrupulousness  can  never  be  associated.  (St. 
Andrews.) 

121.  Either  the  proposition  (S  is  P)  is  true,  or  it  is  not  true;  and 
since  you  must  either  accept  it  as  true  or  deny  it  as  false,  you  can- 
not, logically,  in  any  way  suspend  your  judgment  in  the  matter. 
(St.  Andrews.) 

122.  What  is  the  use  of  all  this  teaching?  Every  day  you 
hear  of  a  fraud  or  forgery,  by  some  one  who  might  have  led  an  inno- 
cent life,  if  he  had  never  learned  to  read  and  write.     (Edinburgh.) 

123.  Pious  men  only  are  fit  to  be  ministers  of  religion;  some 
men  who  have  not  received  a  college  education  are  pious  men, 
therefore  such  men  are  fitted  to  be  ministers  of  religion. 

124.  What  fallacy  did  Columbus  commit  when  he  proved  that 
an  egg  could  stand  on  end?     (Jevons.) 

125.  No  traitor  is  to  be  trusted,  John  is  no  traitor,  and  there- 
fore is  to  be  trusted. 

126.  Against  what  fallacy  does  the  proverb,  'All  that  glitters 
is  not  gold,'  warn  us? 

127.  Livy  describes  prodigies  in  his  history,  therefore  he  is 
never  to  be  believed. 

128.  The  theory  of  evolution  is  true,  for  it  is  accepted  by  every 
scientific  biologist. 

129.  The  theory  of  evolution  is  not  true,  for  it  was  not  accepted 
by  Agassiz,  or  by  Gladstone;  moreover,  you  cannot  accept  this 
doctrine,  for  it  is  disclaimed  by  the  authorities  of  your  church,, 


Questions  and  Exercises  447 

130.  The  advantages  which  would  accrue  to  the  working  classss 
are  not  sufficient  to  justify  Protection,  neither  are  the  advantages 
which  it  would  bring  to  the  farmers  or  the  manufacturers,  or  to 
any  other  class  in  the  community;  Protection,  therefore,  has  not 
enough  advantages  to  justify  it. 

131.  No  man  should  be  punished  if  he  is  innocent;  this  man 
should  not  be  punished ;  therefore  he  is  innocent. 

132.  The  student  of  history  is  compelled  to  admit  the  law  of 
progress,  for  he  finds  that  society  has  never  stood  still. 

133.  I  will  not  do  this  act  because  it  is  unjust ;  I  know  that  it  is 
unjust  because  my  conscience  tells  me  so,  and  my  conscience  tells 
me  so  because  the  act  is  wrong. 

134.  Gold  and  silver  are  wealth;  therefore  the  diminution  of 
the  gold  and  silver  of  the  country  by  exportation  is  a  diminution 
of  the  wealth  of  the  country. 

135.  Nations  are  justified  in  revolting,  when  badly  governed, 
for  every  people  has  a  right  to  a  good  government.     (Edinburgh.) 

136.  When  Croesus  was  about  to  make  war  upon  Cyrus,  King 
of  Persia,  he  consulted  the  oracle  at  Delphi,  and  received  for  an 
answer  that,  if  he  should  wage  war  against  the  Persians,  he  would 
overthrow  a  mighty  empire. 

137.  England  has  a  gold  coinage,  and  is  a  very  wealthy  country, 
therefore  it  may  be  inferred  that  other  countries  having  a  gold 
coinage  will  be  wealthy. 

138.  Your  arguments  against  the  philosophy  of  Hegci  are  of 
no  value ;  for  you  uphold  that  of  Schopenhauer,  which  is  equally 
repugnant  to  common  sense. 

139.  For  those  who  are  bent  on  cultivating  their  minds  by  dili- 
gent study,  the  incitement  of  academical  honours  is  unnecessary; 
and  it  is  ineffectual  for  the  idle,  and  such  as  are  indifferent  to 
mental  improvement;  therefore  the  incitement  of  academical 
honours  is  either  unnecessary  or  ineffectual. 


448  Questions  and  Exercises 

140.  Without  order  there  is  no  living  in  public  society,  because 
the  want  thereof  is  the  mother  of  confusion,  whereupon  division 
of  necessity  followeth ;   and  out  of  division,  destruction. 

141.  If  it  is  always  impossible  not  to  sin,  it  is  always  unjust  to 
punish.  Now  it  is  always  impossible  not  to  sin,  for  all  that  is 
predetermined  is  necessary,  and  all  that  is  foreseen  is  predeter- 
mined, and  every  event  is  foreseen.  Hence  it  is  always  unjust  to 
punish.     (Leibniz,  Theodicy?) 

142.  If  a  gas  is  heated,  its  temperature  rises;  if  its  temperature 
rises,  its  elastic  force  increases;  if  its  elastic  force  increases,  the 
pressure  on  the  walls  of  the  containing  vessel  increases;  there- 
fore if  a  gas  is  heated,  the  pressure  on  the  walls  of  the  containing 
vessel  increases.     (Ray.) 

143.  The  end  of  human  life  is  either  perfection  or  happiness; 
death  is  the  end  of  human  life ;  therefore  death  is  either  perfection 
or  happiness. 

144.  Can  these  three  propositions  be  true  together?  (1)  Only 
mammals  produce  their  young  alive.  (2)  The  duck-mole  is  a 
mammal.  (3)  Among  creatures  that  lay  eggs  are  duck-moles. 
Assuming  (2)  and  (3)  to  be  true,  what  conclusion  follows?  (St. 
Andrews.) 

145.  Theft  is  a  crime;  theft  was  encouraged  by  the  laws  of 
Sparta;  therefore  the  laws  of  Sparta  encouraged  crime.    (Whately.) 

146.  Opium  is  a  poison;  but  physicians  advise  some  of  their 
patients  to  take  opium;  therefore  physicians  advise  some  of  their 
patients  to  take  poison.     (Whately.) 

147.  You  must  believe  yourself  to  be  infallible,  for  you  always 
believe  the  judgment  you  have  formed  to  be  right,  and  he  whose 
judgment  is  always  right,  is  infallible.     (Whately.) 

148.  If  light  consisted  of  material  particles,  it  would  possess 
momentum ;  it  cannot  consist  of  material  particles,  for  it  does  not 
possess  momentum. 


Questions  and  Exercises  449 

149.  This  person  is  very  learned,  and  very  sociable,  hence  it  fol- 
lows that  learning  increases  sociability. 

150.  Why  advocate  socialism?  Until  men  become  morally 
perfect,  it  is  impossible;  when  they  have  become  so,  it  will  be 
unnecessary.  (Edinburgh.)  In  what  ways  could  you  reply  to 
this? 

151.  The  diameter  of  the  earth  is,  in  round  numbers,  forty 
millions  of  feet.  Consequently  the  attraction  of  a  sphere  of  the 
same  mean  density  as  the  earth,  but  one  foot  in  diameter,  will  be 
5000*0000  Part  t'ie  attraction  of  the  earth ;  that  is,  ¥ otoVwo"  of 
the  weight  of  the  body  attracted.  Consequently,  if  we  should 
measure  the  attraction  of  such  a  sphere  of  lead,  and  find  that 
it  was  just  TirovotfoTJ  tnat  °f  tne  weight  of  the  body  attracted, 
we  would  conclude  that  the  mean  density  of  the  earth  was  equal 
to  that  of  lead.  But  the  attraction  is  actually  found  to  be  nearly 
twice  as  great  as  this;  consequently  a  leaden  sphere  is  nearly 
twice  as  dense  as  the  average  of  the  matter  composing  the  earth. 
(Newcomb,  Popular  Astronomy.) 

152.  Mr.  C.  said  that  he  was  certain  that  the  donors  gave  the 
property  to  the  institution  with  a  distinct  and  unanimous  under- 
standing as  to  its  future  use.  The  directors  who  acted  for  the 
institution  in  this  transfer  must  necessarily  have  had  an  under- 
standing, either  the  same  as  that  of  the  donors,  or  different.  If  the 
understanding  of  the  directors  was  the  same  as  that  of  the  donors, 
then  they,  the  former,  were  unquestionably  bound  to  live  up  to 
that  understanding.  If  it  was  different,  then  the  property  was 
conveyed  on  a  misunderstanding,  and  every  dictate  of  honour 
and  fair  play  would  demand  the  return  of  the  property. 

153.  There  is  no  connection  between  sex  and  the  ballot.  If 
woman  is  like  man,  and  it  is  right  for  man  to  vote,  it  must  be 
right  for  woman  to  do  so.  If  woman  is  unlike  man,  he  can  never 
truly  represent  her,  and  she  ought  to  be  allowed  to  represent  herself. 
(From  letter  to  N.  Y.  Times.) 

2Q 


450  Questions  and  Exercises 

154.  The  British  people  are  fed  from  abroad.  Not  only  does 
the  teeming  industry  on  which  the  prosperity  of  the  people  rests 
derive  its  necessary  materials  from  other  countries,  but  the  food 
raised  on  the  islands  is  wholly  insufficient  to  the  daily  require- 
ments of  the  people.  Without  imports  of  food  they  would  in  a 
measurable  period  be  sorely  distressed,  and  ultimately  would 
face  something  very  like  famine.  It  is  on  the  navy,  therefore,  that 
their  very  life  depends. 

155.  When  dealing  with  such  bodies  as  the  sun,  moon,  or  stars, 
the  force  of  gravitation  overpowers  all  other  forces,  and  all  electric 
and  magnetic  attractions  sink  by  comparison  into  insignificance. 
These  tremendous  forces  must  be  transmitted  by  the  ether,  for  there 
is  undoubtedly  a  connecting  link  of  some  kind.  There  can  be  no 
attraction  across  really  empty  space. 

156.  "  The  fundamental  medium  filling  all  space,  if  there  be  such, 
must  be  ultimately  incompressible,  otherwise  it  would  be  composed 
of  parts,  and  we  should  have  to  seek  for  something  still  more 
fundamental  to  fill  the  interstices. "     (Sir  Oliver  Lodge.) 

157.  Only  those  messages  which  have  been  prepaid  will  be 
delivered.  This  message  has  been  prepaid,  and  therefore  it  will  be 
delivered. 

158.  The  right  to  use  and  kill  animals  for  the  relief  and  con- 
venience of  man  is  universally  recognized  throughout  Christen- 
dom and,  in  general,  throughout  the  civilized  world.  Dominion 
over  the  animate  creation  means,  of  course,  the  right  cf  man 
to  use  animals  for  his  own  good;  and  those  who  kill  animals  for 
food  have  a  poor  logical  ground  to  stand  on  when  they  object  to 
the  use  of  animals  for  the  experimentation  in  scientific  laboratories 
by  experts  who  are  aiming  to  discover  remedies  for  the  terrible 
diseases  which  attack  and  destroy  human  life.  Shall  a  man  have 
animals  killed  for  his  nourishment  and  pleasure,  and  object  to 
that  experimental  research  upon  animals  which  has  enabled 
scientific  and  medical  investigators  to  conquer  numerous  diseases? 


Questions  and  Exercises  451 

159.  It  is  not  surprising  that  Senators  X.  and  Y.,  though  pro 
nounced  protectionists,  should  earnestly  support  the  repeal  of  the 
duty  on  hides.  Not  only  are  the  interests  of  their  immediate  con- 
stituents, the  tanners  and  leather  goods  manufacturers  of  their  State, 
enlisted  in  favour  of  this  measure,  but  the  measure  is  in  reality  one 
of  sound  protection,  the  only  kind,  in  fact,  which  any  industry  in 
the  United  States  can  reasonably  ask  for.  Certainly  there  is  no 
way  of  aiding  a  manufacturer  to  meet  competition  more  effectual  or 
more  just  than  to  release  his  materials  from  an  arbitrary  tax. 

160.  The  forces  of  gravitation,  electricity,  etc.,  are  in  constant 
action  between  the  material  bodies  which  make  up  the  universe. 
But  we  are  convinced  that  there  can  be  no  '  action  at  a  distance,' 
that  is,  across  empty  space.  We  are  therefore  confident  that  a 
physical  medium  exists,  which  we  call  ether,  and  which  fills  out 
the  space  between  the  parts  of  grosser  matter,  and  serves  as  the 
medium  of  all  these  forces. 

But  when  we  come  to  consider  the  nature  of  this  medium,  we 
see  that  to  serve  this  function  it  must  have  certain  very  strange 
qualities,  not  to  be  found  elsewhere,  such  as  perfect  continuity, 
absolute  incompressibility,  indefinite  elasticity.  Further,  it  is 
impalpable  and  invisible,  inaccessible  to  our  most  delicate  instru- 
ments. Is  it  not,  then,  a  wonderful  and  mysterious  agent  ?  And 
may  we  act  assent  to  the  words  of  Sir  Oliver  Lodge,  who  says 
that  when  we  once  know  its  secrets :  — 

"I  feel  as  if  it  would  be  no  merely  material  prospect  that  will  be 
opening  on  our  view,  but  some  glimpse  into  a  region  of  the  universe 
which  science  has  never  entered  yet,  but  which  has  been  sought 
from  far,  and  perhaps  blindly  apprehended  by  painter  and  poet, 
by  philosopher  and  saint." 

161.  If  pain  is  long  continued,  it  is  not  severe ;  and  if  it  is  severe, 
it  does  not  last  long.      (Stoic  axiom.) 

162.  "We  are  not  inclined  to  ascribe  much  logical  value  to 
that  analysis  of  the  inductive  method  which  Bacon  has  given.     It 


452  Questions  and  Exercises 

is  indeed  an  elaborate  and  correct  analysis.  But  it  is  an  analysis 
of  that  which  we  are  all  doing  from  morning  to  night,  and  which 
we  continue  to  do  even  in  our  dreams."  (Macaulay,  Essay  on 
Bacon.) 

163.  It  has  been  pointed  out  by  Cohen  that  reasoning  to  the 
following  effect  occurs  in  some  works  on  mathematics:  "A  magni- 
tude required  for  the  solution  of  a  problem  must  satisfy  a  partic- 
ular equation,  and  as  the  magnitude  x  satisfies  this  equation,  it 
is  therefore  the  magnitude  required."  Examine  the  logical  valid- 
ity of  this  argument.     (Jevons.) 

164.  "To  condemn  coalitions  in  the  abstract  is  manifestly 
absurd;  since,  in  a  popular  government,  no  good  can  be  done 
without  concert,  and  no  concert  can  be  obtained  without  compro- 
mise. .  .  .  But  most  peculiarly  inconsistent  and  unreasonable 
is  the  conduct  of  those  who,  while  they  profess  strong  party  feel- 
ings, yet  entertain  a  superstitious  aversion  to  coalitions.  Every 
argument  which  can  be  urged  against  coalitions,  as  such,  is  also 
an  argument  against  party  connections.  Every  argument  by 
which  party  connections  can  be  defended  is  a  defence  of  coalitions. 
What  coalitions  are  to  parties,  parties  are  to  individuals.  The 
members  of  a  party,  in  order  to  promote  some  great  common  object, 
agree  to  waive  all  subordinate  differences.  Men  are  not  thought 
unprincipled  for  acting  thus;  because  it  is  evident  that  without 
such  mutual  self-sacrifices  of  individual  opinion,  no  government 
can  be  formed.  .  .  .  We  must  extend  the  same  indulgence  to  a 
coalition  between  parties.  If  they  agree  on  every  important  prac- 
tical question  ...  no  party  man  can,  on  his  own  principles,  blame 
them  for  uniting."     (Macaulay.) 

165.  The  bill  imposing  a  2  per  cent  tax  upon  the  net  earnings 
of  corporations  is  one  of  those  hybrids  abhorred  by  nature  and 
disliked  by  man.  It  has  a  double  purpose,  the  bringing  of  revenue 
into  the  Treasury  and  the  securing  of  Federal  control  over  corpo- 
rations.    The  two  purposes  are  dissimilar,  unrelated,  and,  if  not 


Questions  and  Exercises  453 

incDmpatible,  are  at  least  so  far  from  kin  that  the  gross  impro- 
priety of  attempting  to  bring  them  together  in  a  statute  is  obvious. 
There  is  no  principle  of  economics,  no  just  principle  or  theory 
of  taxation,  that  warrants  the  singling  out  of  incorporated  business 
interests  from  the  whole  mass  of  business  interests  as  the  subject 
of  this  exaction.  Partnerships  and  individual  concerns  enjoy  the 
same  protection  of  the  laws,  the  same  benefits  of  orderly  Govern- 
ment, that  accrue  to  corporations.     (N.Y.  Times.) 

166.  The  removal  of  a  tyrant  by  assassination  might  at  times 
bring  relief  to  a  whole  nation,  but  we  should  not  for  that  reason 
consider  ourselves  justified  in  setting  apart  a  class  of  men  specially 
licensed  to  remove  objectionable  rulers,  as  we  license  our  vivi- 
sectors  to  do  what  it  is  illegal  for  any  one  else  to  do.  The  carman, 
or  small  tradesman,  who  is  punished  —  quite  rightly  —  for  over- 
working his  horse,  does  not  do  it  for  the  mere  pleasure  of  being 
cruel.  He  may  have  a  famijy  to  support,  and  must  get  all  he  can 
out  of  the  animal,  regardless  of  his  feelings.  In  what  respect  is 
the  vivisectors'  cruelty  different  from  his,  morally?  If  utility, 
consisting  in  diminished  pain  or  increased  pleasure,  carries  moral 
right  with  it,  then  almost  all  cruelty  may  be  defended.  (Letter 
to  Saturday  Review.) 

167.  "  No,  neither  the  uneducated  judgment  nor  the  instincts  of 
the  uneducated  can  ever  come  to  have  more  than  the  very  slightest 
value  in  the  determination  of  what  is  true  or  false  in  art.  A  genuine 
democracy  of  social  condition  may  or  may  not  be  practically  pos- 
sible ;  but  the  democracy  of  intellect,  happily,  is  impossible.  .  .  . 
In  material  matters,  even,  in  matters  most  within  his  reach,  has  the 
labourer  ever  been  able  to  understand  a  machine,  which  he  will 
come  in  time  to  prize  for  its  service,  until  it  has  been  laboriously 
explained  to  him,  and,  for  the  most  part,  forced  upon  him  for 
his  good  ?  How,  then,  is  he  to  understand  a  poem,  which  must 
always  continue  to  seem  to  him  a  useless  thing,  useless  at  all  events 
to  him?"     (Symons.) 


454  Questions  and  Exercises 

168.  "The  fashionable  logic  of  the  Greeks  was  far  from  strict 
Logic  never  can  be  strict  where  books  are  scarce,  and  where 
information  is  conveyed  orally.  We  are  all  aware  how  frequently 
fallacies  which,  when  set  down  on  paper,  are  at  once  detected,  pass 
for  unanswerable  arguments  when  dexterously  and  volubly  urged 
in  Parliament  or  in  private  conversation.  The  reason  is  evident. 
We  cannot  inspect  them  closely  enough  to  perceive  their  inaccuracy. 
We  cannot  readily  compare  them  with  each  other.  .  .  .  Almost 
all  the  education  of  a  Greek  consisted  in  talking  and  listening." 
(Macaulay.) 

169.  [The  "Peculiar  People"  have  got  themselves  into  trouble 
again.  A  coroner's  jury  has  returned  a  verdict  of  manslaughter 
against  two  parents  who  were  prevented  by  religious  scruples  from 
obtaining  medical  assistance  for  their  child.]  .  .  .  But  it  is 
advisable  for  the  State  to  interfere  with  a  course  of  procedure  that 
promises  to  remove  one  of  the  gravest  dangers  of  modern  civilization. 
Anything  which  tends  to  check  over-population  should  recommend 
itself  to  the  careful  consideration  of  political  economists.  And  the 
methods  of  the  "Peculiar  People"  are,  after  all,  nothing  more  than 
a  practical  application  of  the  law  of  evolution.  It  is  only  the  fittest 
who  are  allowed  to  survive,  the  weaklings  are  left  to  die ;  and  it  is 
possible  that  this  sect,  unless  interfered  with,  will  provide  us  with  a 
new  and  sturdy  race  of  men  and  women.  It  may  be  found  more 
expedient  to  encourage  the  "Peculiar  People"  than  to  nip  in  the 
bud  one  of  the  most  promising  remedies  ever  offered  to  suffering 
humanity.     {Saturday  Review.) 

170.  In  "Is  Shakespeare  Dead?"  Mark  Twain  argues  that 
Shakespeare  was  either  a  lawyer  or  not  the  author  of  the  works 
which  go  under  his  name.  To  the  student  of  Shakespeare  this  must 
appear  (with  all  due  respect  to  the  learned  Mr.  Twain)  silly.  Might 
he  not,  with  equal  reason,  claim  that  Shakespeare  must  have  been 
a  doctor,  a  warrior,  a  priest,  a  king,  a  fool,  a  woman,  or  any  other 
of  the  many  types  of  beings  he  so  marvellously  created,  or  else  inca- 


Questions  and  Exercises  455 

pable  of  producing  such  works  ?  In  this  instance,  it  appears  to  me, 
Mark  Twain  has  o'erleaped  himself  and  fallen  on  the  wrong  side 
(Letter  to  N.Y.  Times.) 

171.  If  the  Bible  is  an  inspired  book,  it  ought  to  be  true.  .  .  . 
If  the  Bible  is  true,  slavery  is  right,  and  the  world  should  go  back 
to  the  barbarism  of  lash  and  chain.  If  the  Bible  is  true,  polygamy 
is  the  highest  form  of  virtue.  ...  If  the  Bible  is  true,  the  science 
known  as  astronomy  is  a  collection  of  mistakes.  ...  If  the 
Bible  is  true,  the  science  known  as  geology  is  false  and  every  fossil 
is  a  petrified  perjurer. 

The  defenders  of  orthodox  creeds  should  have  the  courage  to 
candidly  answer  at  least  two  questions:  First,  Is  the  Bible 
inspired?  Second,  Is  the  Bible  true?  And  when  they  answer 
these  questions,  they  should  remember  that  if  the  Bible  is  true,  it 
needs  no  inspiration,  and  that  if  not  true,  inspiration  can  do  it  no 
good.     (R.  G.  Ingersoll.) 

172.  Let  it  be  possible  that  universal  peace  can  be  enforced. 
The  result  would  be  to  petrify  the  present  status  quo,  both  territorial 
and  dynastic,  unless  the  prodigious  task  of  revising  it  were  under- 
taken as  a  preliminary,  in  which  case  peace  might  be  regarded 
as  adjourned  sine  die.  As  for  the  present  status  quo,  there  are 
few  people  indeed  who  would  welcome  its  permanence.  (Saturday 
Review.) 

173.  If  the  principle  be  once  admitted  and  established  that  the 
Federal  Government  may  lay  a  tax  upon  a  corporation  doing  busi- 
ness under  a  State  charter,  there  can  be  no  limitation.  In  Mc- 
culloch vs.  Maryland,  Chief  Justice  Marshall  laid  down  the 
memorable  principle  that  "the  power  to  tax  involves  the  power  to 
destroy,"  and  "the  power  to  destroy  may  defeat  and  render  useless 
the  power  to  create."  If  Congress  may  pass  a  law  levying  a  tax  of 
2  per  cent  upon  corporations  created  by  a  State,  many  of  them 
doing  business  exclusively  within  the  State,  then  it  may  under  the 
principle  enunciated  by  Marshall  impose  a  tax  of  50  or  100  per 


456  Questions  and  Exercises 

cent  upon  the  income  of  such  corporations.  It  may  destro) 
them  altogether,  and  that  means  that  the  enactment  of  this  tax 
bill  sets  up  the  principle  that  the  Federal  Government  may  com- 
pletely annul  the  right  of  a  State  to  create  corporations  and  au- 
thorize them  to  do  business,  a  right  not  derived  from  the  Federal 
Government,  but  possessed  by  the  sovereign  States  before  the 
Federal  Government  was  created.     (N.Y.  Times.) 

174.  Nevertheless,  impertinence  or  not,  pedagogy  ought  to  be 
able  to  show,  if  its  theory  be  true,  that  the  faculties  of  those  trained 
in  the  formal  school  exercises  can  be  successfully  applied  to  the 
various  world  problems.  But  by  this  test  the  folly  of  the  educa- 
tional theory  becomes  manifest.  If  lgebraic  exercises  train  the 
ability  merely  to  solve  algebraic  problems  of  the  same  character  as 
those  used  in  school,  and  do  not  train  the  pupils  in  the  problems 
of  commerce,  government,  society,  morals,  etc.,  the  subject  is  then 
manifestly  worthless  to  the  world,  because  the  world  does  not 
use  school  algebra.  If  Latin  trains  the  faculty  of  discriminating 
differences  only  in  Latin,  and  not  in  world  problems,  then  it  is  con- 
fessedly useless,  because  Latin  genders  are  not  used  by  the  world. 
(F.  Burk.) 

175.  As  to  Mr.  Balfour's  argument  that  legislation  against  im- 
morality can  only  be  of  use  when  there  is  already  some  germ  of 
moral  disapproval  against  the  practice  aimed  at,  it  is  very  likely 
true.  But  this  does  not  touch  the  clauses  against  smoking  by 
children.  There  is  a  very  general  feeling  of  disapproval  of  chil- 
dren smoking,  and  it  is  a  moral  disapproval.  We  see  for  our- 
selves, and  physicians  produce  much  evidence  to  show,  that  smok- 
ing by  children  causes  mental  and  physical  disease,  and  therefore 
what  even  conventionally  we  agree  to  call  strictly  moral  deteriora- 
tion. ...  If  legislation  has  this  germ  to  work  on  for  repressing 
juvenile  smoking,  there  is  as  good  a  priori  argument  for  it  as  in 
any  other  instance  where  legislation  is  applied  to  expand  the  germ 
into  a  fully  developed  moral  rule  of  the  community,  recognized  by 


Questions  and  Exercises  457 

law.  We  do  not  leave  the  germs  to  take  care  of  themselves;  we 
foster  them;  and  morality  is  more  easily  accepted  as  morality 
when  there  is  a  law  at  the  back  of  it.  Most  people  like  to  be  on 
the  side  of  the  law;  it  is  more  respectable.  ...  In  theory  it  is 
very  difficult  to  say  when  the  morality  of  some  should  be  imposed 
on  others;  but  this  is  what  law  generally  comes  to.  It  is  a  moral 
feeling  which  gives  rise  to  the  health  laws;  and  we  impose  them 
on  many  who  think  they  ought  to  do  as  they  like  either  in  ignorance 
or  self-will.  .  .  .  But  the  essential  character  of  a  law  is  that  it  is 
compulsory.  It  is  no  use  passing  it  unless  we  are  prepared  to  apply 
compulsion  at  all  necessary  points.     {Saturday  Review.) 

176.  If  adopted  just  to  avoid  the  appearance  of  charity,  the  Car- 
negie foundation's  plan  to  pension  college  teachers  without  regard  to 
their  private  means  seems  hardly  necessary.  Only  a  few  hyper- 
sensitive souls  insist  upon  viewing  the  endowment  as  a  poor  fund. 
Everybody  else  perceives  that  there  is  no  difference  whatever 
between  money  given  to  a  college  for  a  chair  in  physics,  and  money 
given  for  a  retiring  allowance  to  a  professor  of  physics.  The  man 
who  accepts  as  salary  the  interest  on  the  first  sum  is  just  as  much 
and  just  as  little  an  object  of  charity  as  the  pensioner.  The 
latter  has  infinitely  less  cause  for  humiliation  than  the  well-to-do 
lawyer  who  secures  $5000  worth  of  education  for  his  son  at  a  cost 
of  $600  in  tuition  fees.  The  college  professor  has  earned  his  pen- 
sion by  hard  work ;  it  is  only  deferred  salary.  If  he  cannot  accept 
it  as  such,  consistency  will  force  him  to  resign  at  once ;  for  all  his 
academic  earnings  are  equally  tainted  with  benevolence."  (Na- 
tion.) 

177.  "A  asserts  with  incorrigible  optimism  that  'without  too 
much  you  cannot  have  enough  of  anything.  Lots  of  inferior  books, 
lots  of  bad  statues,  lots  of  dull  speeches,  of  tenth-rate  men  and 
women,  as  a  condition  of  the  few  precious  specimens  in  either 
kind  being  realized.'  As  the  condition,  yes;  but  as  the  cause,  no. 
We  can  never  have  the  precious  things  in  literature  merely  by  add- 
ing to  the  multitude  of  cheap  things."     (Nation.) 


458  Questions  and  Exercises 

What  fallacy  does  this  passage  point  out? 

178.  It  is  difficult  to  deal  with  the  'militant  suffragettes.' 
One  knows  this  difficulty  in  private  life.  Nothing  is  more 
awkward  than  to  be  assaulted  by  a  woman.  Equally  difficult 
is  the  position  for  a  man  whom  a  lady  has  insulted.  He  has 
no  remedy.  This  very  thought,  that  chivalry  forbids  a  man  to 
retaliate,  and  in  many  circumstances  even  to  defend  himself,  will 
usually  make  a  lady  especially  careful  not  to  insult  a  man.  It  is 
the  woman's  side  of  chivalry.  But  chivalry  is  surely  for  men  to 
practise  and  women  to  accept.  Put  "profit  by"  for  "  accept,"  and 
you  get  precisely  the  suffragette  view  of  the  matter.  As  fellow- 
men  they  claim  the  right  to  use  violence;  as  women,  they  claim 
the  right  to  chivalry.  A  moment's  thought  of  the  position  in  which 
they  put  the  police,  for  instance,  —  mere  agents  who  have  no  option 
but  to  do  what  they  are  told,  —  shows  these  women's  tactics  to  be 
mean. 

It  is  in  vain  to  show  them  how  they  are  obstructing  their  own 
cause.  Force  may  be  a  very  good  way  to  attain  your  object,  if 
you  can  get  force  enough  ;  if  you  cannot,  it  is  the  worst  possible  way. 
It  may  always  be  reasonable  for  men  to  resort  to  force ;  they  may 
any  time  be  able  to  compel  where  they  cannot  persuade.  But  for 
women  it  must  always  be  idle.  No  multitudes  of  suffragettes  will 
ever  terrorize,  not  to  speak  of  compelling,  anybody  to  do  anything. 
There  is  nothing  impressive  in  the  sight  of  a  few  excited  women 
hustling  the  police,  or  being  hustled  by  them.  The  suffragette 
leaders  boast  that  their  campaign  of  disorder  has  sent  up  the 
numbers  of  their  organization  by  leaps  and  bounds,  but  this  is 
no  evidence  of  public  conversion  to  votes  for  women.  Make 
yourself  notorious,  and  you  will  always  get  imitators  and  admirers. 
Feathex heads  are  always  drawn  to  public  names  that  figure  in 
police  courts.     (Saturday  Review.) 

179.  "If  young  collegians  from  eighteen  to  twenty-two  do  not 
find  in  college  a  chance  for  a  serious,  unbiassed  scrutiny  of  letters 


Questions  and  Exercises  459 

or  philosophy  or  history  or  science,  in  nine  cases  out  of  ten  they  will 
never  again  get  the  opportunity ;  and,  so  far  as  the  real  purpose  of 
university  life  is  concerned,  they  might  better  waste  their  time  and 
their  father's  money  at  home.  Bitter  experience  of  the  present 
generation  of  college  life  goes  far  to  justify  what  we  were  rashly 
inclined  to  regard  as  the  amiable  or  picturesque  crotchets  of  early 
educators.  It  was  not  without  a  substantial  reason  that  colleges 
originally  took  on  the  semi-monastic  mode  of  life,  with  a  common 
garb,  a  common  meal,  and  a  communal  life.  It  segregated  the 
scholar  from  the  world  during  his  scholastic  apprenticeship,  and 
reduced  distinctions  to  a  minimum  within  the  cloister.  It  may 
seem  a  far  call  from  the  mediaeval  college  to  our  military  academy 
at  West  Point,  but  the  scheme  of  social  organization  is  not  dis- 
similar. The  uniform  donned  at  entrance  amalgamates  into  a 
common  body  the  farmer's  son  and  the  financier's  heir.  The  mess 
table  and  the  barracks  life  do  not  reduce  the  cadets  to  a  dead  level, 
but  make  for  the  emergence  of  real,  not  fictitious,  merit.  The 
unquestioned  efficiency  of  West  Poir .„  as  an  educational  machine 
is  in  large  part  traceable  to  a  modern  adherence  to  tried  educa- 
tional methods  of  the  past,  and  to  an  enforced  exclusion  of 
parasitic  interests  that  infest  our  colleges  and  universities." 
(Nation.) 

180.  "  (The  constitution)  has  made  treaties  part  of  our  municipal 
law ;  but  it  has  not  assigned  to  them  any  particular  degree  of  author- 
ity, nor  declared  that  laws  so  enacted  shall  be  irrepealable.  No 
supremacy  is  assigned  to  treaties  over  acts  of  Congress.  That  they 
are  not  perpetual,  and  must  be  in  some  way  repealable,  all  will 
agree.  If  the  president  and  the  senate  alone  possess  the  power 
to  repeal  or  abrogate  the  law  found  in  a  treaty,  inasmuch  as  they 
can  change  or  abrogate  one  treaty  only  by  making  another  incon- 
sistent with  the  first,  the  government  of  the  United  States  could  not 
act  at  all  to  that  effect  without  the  consent  of  some  foreign  govern- 
ment.    I  do  not  consider  —  I  am  not  aware  that  it  has  ever  been 


460  Questions  and  Exercises 

considered  —  that  the  constitution  has  placed  our  country  in  this 
helpless  condition.  ...  If,  therefore,  it  were  admitted  that  the 
treaty  between  the  United  States  and  France  did  contain  an  express 
stipulation  that  the  United  States  would  not  exclude  slavery  from 
(the  Louisiana  Purchase),  the  Supreme  Court  could  not  declare 
that  an  act  of  Congress  excluding  it  was  void  by  reason  of  the 
treaty."     (B.  R.  Curtis.) 

181.  "Our  ideas  reach  no  farther  than  our  experience.  We 
have  no  experience  of  divine  attributes  and  operations.  I  need  not 
conclude  my  syllogism.  You  can  draw  the  inference  yourself." 
(Hume.) 

182.  "  No  one  would  be  so  foolish  as  to  argue  that  English  has  not 
profited  by  these  communions  with  the  other  great  literatures  of 
the  world.  On  the  intellectual  side  the  profit  is  incalculably  great. 
Abundance,  richness,  flexibility,  tolerance,  colour,  range,  are  all  cos- 
mopolitan qualities  which,  in  great  measure,  English  literature  pos- 
sesses. Yet  to  have  all  these  without  national  virtues  profiteth 
nothing;  and  it  is  only  when  a  literature  begins  to  lay  aside  its 
national  virtues  and  becomes  to  a  certain  extent  unmoral,  or  even 
immoral,  that  it  enters  triumphantly  upon  the  conquest  of  the 
world.  ...  It  almost  seems  that  the  qualities  which  make  for 
the  federation  of  the  world  are  not  the  national  virtues,  but  the 
international  vices.  ...  A  world-language  has  terrible  things  to 
express.  If  English  does  not  wish  to  become  a  vessel  of  wrath,  it 
had  better  not  dwell  too  long  on  its  imperialistic  dreams.  It  had 
better  come  home  and  fight  for  its  altars  and  its  fires,  and  revive 
its  healthy  loves  and  hates.  .  .  .  Cosmopolitanism  is  a  dear 
teacher,  and  the  pith  of  its  lesson  is  only  this :  A  man  cannot  be 
all  things  to  all  men  and  be  much  of  a  man  himself."     (Nation.) 

183.  Are  we  justified  in  saying  that  the  Catholic  Church  is  of 
divine  origin  because  the  Pagans  failed  to  destroy  it  by  persecu- 
tion? 

We  will  put  the  Cardinal's  statement  in  form:  — 


Questions  and  Exercises  461 

Paganism  failed  to  destroy  Catholicism  by  persecution;  therefore 
Catholicism  is  of  divine  origin.  Let  us  make  an  application  of 
this  logic.  Catholicism  failed  to  destroy  Protestantism  by  perse- 
cution; therefore  Protestantism  is  of  divine  origin.  Catholicism 
and  Protestantism  united  failed  to  destroy  Infidelity;  therefore 
Infidelity  is  of  divine  origin.  Let  us  make  another  application. 
Paganism  did  not  succeed  in  destroying  Catholicism;  therefore 
Paganism  was  a  false  religion.  Catholicism  did  not  succeed  in 
destroying  Protestantism;  therefore  Catholicism  is  a  false  religion. 
Catholicism  and  Protestantism  combined  failed  to  destroy  Infi- 
delity; therefore  both  Catholicism  and  Protestantism  are  false 
religions.     (Reply  of  R.  G.  Ingersoll  to  Cardinal  Manning.) 

184.  Nothing  is  demonstrable,  unless  the  contrary  implies  a 
contradiction.  Nothing  that  is  distinctly  conceivable  implies  a 
contradiction.  Whatever  we  conceive  as  existent,  we  can  also 
conceive  as  non-existent.  There  is  no  being,  therefore,  whose 
non-existence  implies  a  contradiction.  Consequently,  there  is 
no  being  whose  existence  is  demonstrable.     (Hume.) 

185.  "  The  purpose  (of  war)  is  to  be  secured  by  a  coercion  of  the 
power  against  which  you  act.  The  customs  and  opinions  of  mod- 
ern civilization  have  recognized  certain  modes  of  coercing  the 
power  you  are  acting  against  as  justifiable.  Injury  to  private 
persons  or  their  property  is  avoided  as  far  as  it  reasonably  can  be 
done.  Wherever  private  property  is  taken  or  destroyed,  it  is  be- 
cause it  is  of  such  a  character,  or  so  situated,  as  to  make  its  capture 
a  justifiable  means  of  coercing  the  power  with  which  you  are  at 
war.  .  .  .  But  the  humanity  of  modern  times  has  abstained 
from  the  taking  of  private  property  not  liable  to  use  in  war.  when 
on  land.  Some  of  the  reasons  for  this  are  the  infinite  varieties  of 
its  character,  the  difficulty  of  discriminating  among  these  varieties, 
the  need  of  much  of  it  to  support  the  life  of  non-combatant  persons 
and  animals,  and,  above  all,  the  moral  dangers  attending  searches 
and  captures  in  households.     But  on  the  high  seas  these  reasons 


462  Questions  and  Exercises 

do  not  apply.  Strictly  personal  effects  are  not  taken.  Merchan 
dise  sent  to  sea  is  sent  voluntarily  embarked  by  merchants  on  an 
enterprise  of  profit,  taking  the  risk  in  the  custody  of  men  trained 
and  paid  for  the  business,  and  its  value  is  usually  capable  of  com- 
pensation in  money."     (R.  H.  Dana.) 

186.  "  The  literature  which  makes  aesthetic  gratification  the  end 
of  existence  defeats  its  own  end.  Pursued  as  an  ultimate  goal, 
it  leads  sooner  or  later  into  quagmires.  The  aesthete  wanders 
from  home  in  the  quest  of  new  and  strange  beauties.  His  truant 
feet  stray  from  .  .  .  the  sound  to  the  unsound,  and  thence  to  the 
insane;  from  the  chaste  to  the  unchaste,  and  thence  to  the  inde- 
cent. Yet  the  price  of  illicit  aesthetic  pleasure  is  the  loss  of  all 
aesthetic  pleasure.  The  unhappy  man,  as  M.  Lecomte  says, 
who  little  by  little  allows  himself  to  be  soiled  with  all  that  filth, 
becomes  finally  insensible  to  a  vigorous  thought,  an  expressive 
portrait,  or  the  proud  wing  of  poetry."     (Nation.) 

187.  "  The  attorney-general  tells  us  that  all  persons  whom  he  and 
his  associates  choose  to  denounce  for  giving  aid  to  the  rebellion  are 
to  be  treated  as  being  themselves  a  part  of  the  rebellion  —  they  are 
public  enemies,  and  therefore  they  may  be  punished  without  being 
found  guilty  by  a  competent  court  or  jury.  This  convenient 
rule  would  outlaw  every  citizen  the  moment  he  is  charged 
with  a  political  offence.  But  political  offenders  are  precisely 
the  class  of  persons  who  most  need  the  protection  of  a  court 
and  jury,  for  the  prosecutions  against  them  are  most  likely 
to  be  unfounded  both  in  fact  and  in  law.  Whether  innocent 
or  guilty,  to  accuse  is  to  convict  them  before  the  ignorant 
and  bigoted  men  who  generally  sit  in  military  courts.  But 
this  court  decided  in  the  Prize  Cases  that  all  who  live  in  the 
enemy's  territory  are  public  enemies,  without  regard  to  their  per- 
sonal sentiments  or  conduct;  and  the  converse  of  the  statement  is 
equally  true,  —  that  all  who  reside  inside  of  our  own  territory  are 
to  be  treated  as  under  the  protection  of  the  law.     If  they  help  the 


Questions  and  Exercises  463 

enemy,  they  are  criminals ;  but  they  cannot  be  punished  without 
legal  conviction."     (Jeremiah  S.  Black.) 

Analyze  the  above  passage  carefully. 

Is  what  Justice  Black  calls  'the  converse  of  the  statement'  its 
!ogical  converse?  And,  if  not,  can  it  be  derived  from  the  first 
statement  by  any  of  the  processes  of  '  immediate  inference  '  ? 

188.  We  should  limit  public  expenditures  to  public  purposes. 
Take  as  little  as  possible  out  of  the  pocket  of  the  tax-payer,  and 
use  what  is  taken  only  for  the  purposes  which  can  be  justified 
on  public  grounds.  What  will  happen  if  you  go  on  the 
contrary  principle  —  a  principle  which  the  Socialists  adopt 
and  which  some  semi-Socialists  sympathize  with  —  the  prin- 
ciple that  it  is  just  to  use  taxation  as  a  means  of  equalizing  the 
inequalities  of  fortune  ?  Surely  if  that  principle  obtains,  the  people 
will  learn  that  their  prosperity  is  to  be  secured,  not  by  their  own 
industrial  efforts,  but  by  their  political  exertions ;  politics  will  be- 
come a  game  of  grab  if  you  once  admit  that  the  State  is  justified  in 
taking  from  A  for  the  private  benefit  of  B.  There  is  no  end  to  the 
demands  that  may  then  be  made,  except  this,  that  the  State  will 
be  ruined  because  everybody,  instead  of  working  for  himself,  will 
be  seeing  how  much  he  can  steal  from  the  State.  (Quoted  by 
N.  Y.  Times.) 

189.  Mr.  X.  was  as  impertinent  as  he  was  arrogant  in  taunting 
his  Republican  opponents  with  wishing  to  form  a  new  party.  He 
assumes  that  anybody  who  will  not  accept  his  interpretation  of 
the  tariff  policy  of  the  party  to  which  he  professes  to  belong  is 
disloyal.  He  chooses  to  forget  that  the  men  who  hold  to  his  inter- 
pretation were  badly  beaten  at  the  last  National  Convention,  and 
that  the  Senators  who  are  opposing  him  are  faithfully  trying  to 
carry  out  the  specific  pledges  of  the  party  made  at  that  convention. 
If  they  are  to  be  denounced,  an  entirely  new  system  of  party  dis- 
cipline and  obligation  must  be  devised  under  which  fidelity  is 
punished  as  betrayal,  and  treachery  is  rewarded  with  undisputed 


464  Questions  and  Exercises 

power.  By  that  system  Mr.  Taft,if  he  remains  as  true  to  the  Repub- 
lican pledges  in  action  as  he  has  so  far  in  profession,  must  be  read 
out  of  his  party.  This  is  the  practical  outcome  of  the  position. 
From  the  standpoint  of  party  expediency  it  is  as  risky  as  from 
the  point  of  view  of  principle  it  is  immoral.     (N.  Y.  Times.) 

190.  If  the  average  mental  development  reached  by  the  Greeks 
was  .  .  .  not  only  in  excess  of  that  of  those  modern  European  races 
whose  civilization  is  reaching  such  an  ascendency  in  the  world  to-day, 
but  ...  as  far  above  it  as  the  mental  ability  of  these  latter  is  above 
that  of  some  of  the  lowest  of  the  peoples  whom  they  have  displaced 
through  the  operation  of  natural  selection,  then  it  seems  extremely 
difficult  to  reconcile  this  fact  with  an  unshaken  belief  in  any  theory 
according  to  which  intellectual  development  must  be  taken  as  the 
dominant  factor  in  human  evolution.  We  may  be  prepared  to 
accept  Sir  Henry  Maine's  view  that  in  an  intellectual  sense  nothing 
moves  in  this  Western  world  that  is  not  Greek  in  its  origin ;  but  no 
homage  of  this  kind  to  the  Greek  intellect,  however  well  it  may  be 
deserved,  can  blind  our  eyes  to  the  fact  that  the  Greek  peoples 
themselves,  like  the  ancient  Romans,  have  absolutely  disappeared  in 
the  human  struggle  for  existence.  Even  their  blood  cannot  be  dis- 
tinguished in  the  populations  of  large  tracts  of  Eastern  and  Southern 
Europe,  and  Western  Asia,  where  these  ruling  races  were  once 
predominant  in  numbers  and  influence.     (Benjamin  Kidd.) 

PART  II.  —  Inductive  Methods 

Chapter  XIII.  —  The  Problem  of  Induction 

1.  Explain  why  syllogistic  logic  is  not  a  complete  account  of  the 
nature  of  thinking. 

2.  Give  a  statement  of  the  general  problem  of  Induction.     Why 
is  there  any  problem  in  the  case? 

3.  Explain  the  distinction  between  Induction  by  Enumeration, 
ind  Induction  by  Analysis. 


Questions  and  Exercises  465 

4.  Explain  the  following  terms :  Induction  by  Simple  Enumera- 
tion, Prerogative  Instances,  and  Crucial  Experiments. 

5.  What  rules  may  be  given  for  the  selection  of  instances  in  an 
inductive  investigation  ? 

6.  It  is  sometimes  said  that  Elimination  is  the  essential  principle 
of  Induction.     Discuss  this  statement. 

7.  Explain  the  function  of  Analogy  and  Hypotheses  in  Induc- 
tion. 

Chapter  XIV 

1.  What  is  the  general  assumption  of  all  Inductive  thinking? 
Explain  the  relation  of  this  assumption  to  the  laws  of  Thought. 

2.  What  is  meant  by  a  category  of  Thought?  Illustrate.  What 
is  the  distinction  between  .a  '  dynamic  '  and  a  '  static '  category? 

3.  What  is  to  be  said  regarding  the  division  of  Inductive  meth- 
ods into  methods  of  Observation,  and  methods  of  Explanation? 
Would  it  be  permissible  to  add  Experimental  methods  as  a  third 
and  independent  class? 

4.  Explain  the  relation  between  facts  and  theories. 

5.  What  is  the  distinction  between  'empirical'  and  'scientific' 
knowledge  ? 

Chapter  XV.  —  Enumeration  and  Statistics 

1.  What  is  the  justification  for  beginning  our  account  of  the 
inductive  methods  with  Enumeration? 

2.  Explain  how  it  is  sometimes  possible  to  reach  certain  con- 
clusions on  the  basis  of  instances.  In  what  respect  are  such  con- 
clusions defective? 

3.  For  what  purpose  are  Statistics  employed?  To  what  classes 
of  phenomena  are  they  applied?  Explain  the  statement  that 
Statistics  are  valuable  only  when  compiled  intelligently. 

4.  State  and  distinguish  three  uses  to  which  Statistics  may  be 
put. 

2H 


466  Questions  and  Exercises 

5.  Explain  how  Statistics  may  suggest  causal  laws,  or  confirm 
our  expectation  of  them.  May  Statistics  also  be  used  to  disprove 
a  proposed  law  of  causal  connection?     Illustrate  your  answer. 

6.  Explain  what  is  meant  by  the  'average,'  the  'mean,'  and  the 
'  mode,'  and  show  how  each  is  obtained. 

7.  How  does  the  procedure  of  insurance  companies  differ  from 
gambling  ? 

Chapter  XVI.  —  Causal  Determination 

1.  What  are  the  two  main  principles  upon  which  the  canons 
proposed  by  Mill  are  founded? 

2.  Give  the  canon  of  the  method  of  Agreement,  and  illustrate 
its  use. 

3.  'I  have  noticed  that  A  always  precedes  B ;  it  is  therefore  the 
cause  of  B.'     Is  this  good  reasoning?  ■ 

4.  What  is  meant  by  the  'Plurality  of  Causes'  and  by  the 
'Reciprocity  of  Causes'? 

5.  Under  what  disadvantages  does  the  method  of  Agreement 
labour?     How  is  it  supplemented? 

6.  State  and  illustrate  the  canon  of  the  method  of  Difference. 

7.  Why  is  this  method  applicable  only  to  the  spheres  where 
experiment  can  be  employed  ?  Would  it  be  safe  to  depend  upon 
this  method  in  determining  the  causes  of  social  or  political  con- 
ditions? 

8.  How  might  the  canons  of  Agreement  and  Difference  re- 
spectively be  stated  negatively,  as  principles  of  Elimination? 
Would  this  statement  do  full  justice  to  the  inductive  procedure 
involved  ? 

Chapter  XVII.  —  Causal  Determination  {continued) 

1.  Where  do  we  employ  the  Joint  method? 

2.  What  precisely  would  it  be  necessary  to  establish  in  order  to 
establish  inductively  that  some  change  in  the  tariff  laws  was  bene- 
ficial to  the  country  ? 


Questions  and  Exercises  467 

3.  Explain  what  qualifications  it  is  necessary  to  introduce  in 
interpreting  Mill's  statement  of  the  Joint  method. 

4.  'One  of  the  main  characteristics  of  modern  science  is  its 
quantitative  nature.'     Explain. 

5.  How  does  the  law  of  Concomitant  Variations  assist  us  in 
determining  causal  relations? 

6.  In  what  two  ways  may  the  method  of  Residues  be  applied? 

7.  Mention  some  discoveries  to  which  the  investigation  of  un- 
explained residues  has  led. 

Chapter  XVIII.  —  Analogy 

1.  Why  do  we  include  Analogy  among  the  methods  of  Ex- 
planation ? 

2.  What  do  you  mean  by  Analogy  ?  What  is  the  principle  upon 
which  it  proceeds  ? 

3.  How  is  the  word  used  in  mathematical  reasoning,  and  in 
physiology  ? 

4.  Into  what  Figure  of  the  Syllogism  does  an  argument  from 
Analogy  naturally  fall?  Is  the  argument  formally  valid,  and  if 
not,  to  what  syllogistic  fallacy  does  it  correspond? 

5.  Explain  how  Analogy  may  suggest  a  true  law  or  explanatory 
principle. 

6.  Why  do  we  speak  of  Analogy  as  Incomplete  Explanation? 

7.  If  all  analogical  reasoning  yields  only  probability,  is  not  one 
analogy  as  good  as  another  for  purposes  of  inference?  If  not, 
upon  what  does  the  value  of  an  inference  from  Analogy  depend? 

Chapter  XIX.  —  The  Use  of  Hypotheses 

1.  How  do  you  distinguish  the  terms  'theory'  and  'hypothesis'? 

2.  What  is  an  hypothesis,  and  how  is  it  used? 

3.  Do  hypotheses  play  any  part  in  assisting  Observation? 
Explain  and  illustrate. 

4.  Give  some  instances  in  which  hypotheses  have  proved  in- 
jurious, and  have  misled  people  regarding  the  nature  of  facts. 


468  Questions  and  Exercises 

5.  'Hypotheses  are  formed  by  the  imagination  working  in 
dependence  upon  facts  and  guided  by  analogy.'     Explain. 

6.  What  are  the  steps  in  the  proof  of  an  hypothesis? 

7.  Explain  what  part  is  played  by  Induction  and  Deduction 
respectively  in  using  hypotheses. 

8.  What  part  does  Elimination  play  in  the  proof  of  an  hypothe- 
sis? Explain  the  nature  of  the  formal  fallacy  involved  in  the 
statement  that  an  hypothesis  is  established  when  its  results  are 
shown  to  be  true.     How  is  this  difficulty  overcome? 

9.  What  canons  have  been  laid  down  to  which  a  good  hy- 
pothesis must  conform?  Why  are  the  first  and  third  of  these 
rules  of  little  value  ? 

10.  Explain  why  an  unverifiable  hypothesis  is  not  worth   dis- 
cussing. 

Chapter  XX.  —  Fallacies  of  Induction 

1.  What  is  the  source  of  fallacy?  How  far  is  it  true  that  the 
study  of  Logic  can  protect  us  from  fallacies  ? 

2.  How  do  you  classify  Inductive  Fallacies? 

3.  Explain  and  illustrate  the  following  fallacies:  Question- 
begging  Epithet,  Equivocation,  Fallacies  due  to  Figurative  Lan- 
guage. 

4.  Explain  and  illustrate  the  tendency  of  the  mind  to  neglect 
negative  cases. 

5.  Is  it  an  easy  matter  to  'tell  just  what  we  saw  and  heard'  at  a 
particular  time? 

6.  What  do  you  mean  by  post  hoc  ergo  propter  hoc  ?  Why  may 
we  take  this  as  the  general  type  of  inductive  fallacies  ? 

7.  What  did  Bacon  mean  by  the  Idols  of  the  Cave,  of  the 
Tribe,  of  the  Market-Place,  of  the  Theatre? 

8.  'Every  age,  as  well  as  every  individual,  has  its  idols.'  Ex- 
plain this  statement. 


Questions  and  Exercises  469 

Miscellaneous  Examples  of  Inductive  Arguments 

Analyze  the  examples  of  inductive  reasoning  given  below,  and 
point  out  what  methods  are  employed,  indicating  also  whether  or 
not  the  conclusion  is  completely  established,  and  naming  the 
fallacy,  if  any  be  present :  — 

1.  In  my  experience  A  has  been  invariably  preceded  by  B,  and 
we  may  therefore  conclude  that  B  is  the  cause  of  A. 

2.  Scarlet  poppies,  scarlet  verbenas,  the  scarlet  hawthorn,  and 
honeysuckle  are  all  odourless,  therefore  we  may  conclude  that  all 
scarlet  flowers  are  destitute  of  odour. 

3.  What  inference,  if  any,  can  be  drawn  from  the  following 
statement:  'In  nine  counties,  in  which  the  population  is  from  100 
to  150  per  square  mile,  the  births  are  296  to  100  marriages;  in 
sixteen  counties,  with  a  population  of  150  to  200  per  square  mile, 
the  births  are  308  to  100  marriages'? 

4.  The  great  famine  in  Ireland  began  in  1845  and  reached  its 
climax  in  1848.  During  this  time  agrarian  crime  increased  very 
rapidly,  until,  in  1848,  it  was  more  than  three  times  as  great  as  in 
1845.  After  this  time  it  decreased  with  the  return  of  better  crops, 
until,  in  1851,  it  was  only  50  per  cent  more  than  it  was  in  1845. 
It  is  evident  from  this  that  a  close  relation  of  cause  and  effect  exists 
between  famine  and  agrarian  crime.     (Hyslop.) 

5.  Sachs  maintained,  in  1862,  that  starch  is  formed  by  the 
decomposition  in  chlorophyl  of  carbon-dioxide  gas  under  the 
influence  of  light.  He  found  that  when  all  other  conditions  were 
constant,  and  light  was  excluded  from  a  plant,  no  starch  was 
formed;  the  single  circumstance  of  readmitting  light  was  accom- 
panied by  renewed  formation  of  starch.  Further,  he  found  that  if 
certain  portions  of  the  leaves  of  an  illuminated  plant  were  covered 
with  black  paper,  no  starch  was  found  in  these  portions. 

6.  Jupiter  gives  out  more  light  than  it  receives  from  the  sun. 
What  is  the  obvious  conclusion,  and  by  what  method  is  it  reached  ? 


4^0  Questions  and  Exercises 

7.  What  methods  would  you  employ  in  order  to  test  the  truth 
of  the  proposition,  omne  vivum  ex  vivo  ? 

8.  It  is  evident  that  the  green  colour  of  plants  holds  some  neces- 
sary relation  to  light,  for  the  leaves  of  plants  growing  in  the  dark, 
as  potatoes  sprouting  in  a  cellar,  do  not  develop  this  colour.  Even 
when  leaves  have  developed  the  green  colour,  they  lose  it  if  deprived 
of  light,  as  is  shown  by  the  process  of  blanching  celery  and  by  the 
effect  on  the  colour  if  a  board  has  lain  upon  it  for  a  long  time. 
(Coulter.) 

9.  Another  indication  that  the  green  colour  is  connected  with 
light  may  be  obtained  from  the  fact  that  it  is  found  only  in  the  sur- 
face region  of  plants.  If  one  cuts  across  a  living  twig  or  into  a 
cactus  body,  the  green  colour  will  be  seen  only  in  the  outer  part  of 
the  section.     (Coulter.) 

10.  If  an  active  leaf  or  water  plant  be  submerged  in  water  in 
a  glass  vessel  and  exposed  to  the  light  bubbles  may  be  seen  com- 
ing from  the  leaf  surface  and  rising  through  the  water.  The 
water  is  merely  a  device  by  which  the  bubbles  of  gas  may  be 
seen.  If  the  leaf  is  very  active,  the  bubbles  are  numerous. 
That  this  activity  holds  a  definite  relation  to  light  may  be  proved 
by  gradually  removing  the  vessel  containing  the  leaf  from  the 
light.  As  the  light  diminishes  the  bubbles  diminish  in  number, 
and  when  a  certain  amount  of  darkness  has  been  reached  the 
bubbles  will  cease  entirely.  If  now  the  vessel  be  brought  back 
gradually  into  the  light,  the  bubbles  will  reappear,  more  and 
more  numerous  as  the  light  increases.     (Coulter.) 

11.  War  is  a  blessing,  not  an  evil.  Show  me  a  nation  that  has 
ever  become  great  without  bloodletting. 

12.  If  wages  depend  upon  the  ratio  between  the  amount  of 
labour-seeking  employment,  and  the  amount  of  capital  devoted  to 
ks  employment,  the  relative  scarcity  or  abundance  of  one  factor 
must  mean  the  relative  abundance  or  scarcity  of  the  other.  Thus 
capital  must  be  relatively  abundant  where  wages  are  high,  and 


Questions  and  Exercises  471 

relatively  scarce  where  wages  are  low.  Now,  as  the  capital  used 
in  paying  wages  must  largely  consist  of  the  capital-seeking  invest- 
ment, the  current  rate  of  interest  must  be  the  measure  of  its  rela- 
tive abundance  or  scarcity.  So  if  it  be  true  that  wages  depend 
upon  the  ratio  between  the  amount  of  labour-seeking  employment, 
and  the  capital  devoted  to  its  employment,  then  high  wages  must 
be  accompanied  by  low  interest,  and,  reversely,  low  wages  must  be 
accompanied  by  high  interest.  This  is  not  the  fact  but  the  con- 
trary.    (George.) 

13.  Construct  an  inductive  argument  to  prove  that  some  article 
of  food,  or  some  habit,  is  beneficial  or  injurious  to  you,  and  analyze 
your  reasoning,  showing  the  methods  which  you  have  employed. 

14.  Some  comets  have  been  observed  to  have  the  same  orbits 
as  certain  meteoric  showers.  The  hypothesis  is  suggested  that  all 
meteoric  showers  may  represent  the  debris  of  disintegrated  comets. 
Biela's  comet  having  been  missing  for  some  time,  it  was  accord- 
ingly predicted  that  when  next  due  it  would  be  replaced  by  a  mete- 
oric shower.     This  prediction  was  verified  by  observation. 

15.  Tyndall  found  that  of  twenty-seven  sterilized  flasks  con- 
taining infusion  of  organic  matter,  and  opened  in  pure  Alpine  air, 
not  one  showed  putrefaction;  while  of  twenty-three  similar  flasks, 
opened  in  a  hayloft,  only  two  remained  free  from  putrefaction 
after  three  days.  He  concluded  that  putrefaction  is  due  to  float- 
ing particles  in  the  air. 

16.  The  census  of  1890  regards  immigration  as  the  sufficient 
explanation  of  the  excess  of  males  over  females  in  the  population 
of  the  United  States.  The  results  of  the  same  census  yield  the 
following  figures:  The  excess  of  white  native  males,  both  parents 
native,  was  587,458.  That  of  white  native  males,  one  or  both 
parents  foreign-born,  was  59,467.  Coloured  native  females  were  in 
excess  of  males  by  18,128.  Foreign-born  white  males  exceeded 
females  by  781,429,  and  foreign-born  coloured  males  were  in  excess 
by  102,864.    What  is  the  bearing  of  these  figures  upon  the  explanar 


472  Questions  and  Exercises 

tion  given  by  the  census,  and  do  they  confirm  or  disprove  it! 
(Willcox.) 

17.  Regarding  our  social  systems  as  organic  growths,  there 
appears  to  be  a  close  analogy  between  their  life-history  and  that 
of  organic  forms  in  general.  We  have,  on  the  one  side,  in  the 
ethical  systems  upon  which  they  are  founded,  the  developmental 
force  which  sets  in  motion  that  life-continuing,  constructive  pro- 
cess which  physiologists  call  anabolism.  On  the  other  side,  and 
in  conflict  with  it,  we  have  in  the  self-assertive  rationalism  of  the 
individual,  the  tendency  —  by  itself  disintegrating  and  destructive 
—  known  as  catabolism.  In  a  social  system,  as  in  any  other  organ- 
ism, the  downward  stage  towards  decay  is  probably  commenced 
when  the  catabolic  tendency  begins  to  progressively  overbalance 
the  anabolic  tendency.     (Benjamin   Kidd.) 

18.  For  many  generations  the  people  of  the  Isle  of  St.  Kilda 
believed  that  the  arrival  of  a  ship  in  the  harbor  inflicted  on  the 
islanders  epidemic  colds  in  the  head,  and  many  ingenious  reasons 
were  devised  why  the  ship  should  cause  colds.  At  last  it  occurred 
to  somebody  that  the  ship  might  not  be  the  cause  of  the  cold,  but 
that  both  might  be  effects  of  some  other  common  cause,  and  it 
was  then  remembered  that  a  ship  could  only  enter  the  harbor 
when  there  was  a  strong  northeast  wind  blowing. 

19.  Schwabe,  observing  sun-spots  for  many  years,  discovered 
that  they  reached  a  maximum,  roughly  speaking,  once  in  every 
ten  years.  In  1851,  Lamont,  reviewing  a  series  of  magnetic  obser- 
vations carried  on  from  1835  to  1850,  perceived  with  some  sur- 
prise that  they  gave  unmistakable  indications  of  a  period  of  \o\ 
years,  during  which  the  range  of  the  daily  variation  of  the  mag- 
netic needle  increased  and  diminished  once.  In  the  following 
winter,  Sir  Edward  Sabine,  ignorant  as  yet  of  Lamont's  conclu- 
sions, undertook  to  examine  a  totally  different  set  of  observations 
concerning  magnetic  '  storms. '  Once  in  about  ten  years  magnetic 
disturbances  were  perceived  to  reach  a  maximum  of  violence  and 


Questions  and  Exercises  473 

frequency.  Sabine  was  the  first  to  note  the  coincidence  between 
this  unlooked-for  result  and  Schwabe's  sun-spot  period.  He 
showed  that,  so  far  as-  observation  had  yet  gone,  the  two  cycles  of 
change  agreed  perfectly  both  in  duration  and  phase,  maximum 
corresponding  to  maximum,  minimum  to  minimum.  What  the 
nature  of  the  connection  could  be  that  bound  together  by  a  common 
law  effects  so  dissimilar  was,  and  still  remains,  beyond  the  reach  of 
well-founded  conjecture;  but  the  fact  was  from  the  first  unde- 
niable.    (Clerke,  History  of  Astronomy.) 

20.  Prior  to  1668  the  spontaneous  generation  of  life  was  com- 
monly accepted  by  naturalists,  and  the  origin  of  maggots  in  decay- 
ing substances  was  regarded  as  an  evidence  of  it.  But  in  that  year 
Redi,  an  Italian  scientist,  exposed  meat  in  jars,  some  of  which 
were  left  uncovered,  some  covered  with  parchment,  and  others  with 
wire  gauze.  The  meat  in  all  these  vessels  became  spoiled,  and  flies, 
being  attracted  by  the  smell  of  decaying  meat,  laid  eggs  in  that 
which  was  exposed,  and  there  came  from  it  a  large  crop  of  mag- 
gots. The  meat  which  was  covered  by  parchment  also  decayed  in 
a  similar  manner,  without  the  appearance  of  maggots  within  it;  and 
in  those  vessels  covered  by  wire  netting  the  flies  laid  their  eggs  upon 
the  wire  netting.  There  they  hatched,  and  the  maggots,  instead 
of  appearing  in  the  meat,  appeared  on  the  surface  of  the  wire  gauze. 
From  this  Redi  concluded  that  maggots  arise  in  decaying  meat 
from  the  hatching  of  the  eggs  of  insects.    (Locy,  Makers  of  Biology.) 

21.  In  1675  Leeuwenhoek  discovered  infusoria,  or  animalcula 
under  the  microscope,  and  it  was  thought  that  such  minute  organ- 
isms as  these  might  be  spontaneously  generated,  even  if  the  larger 
were  not.  About  1745  Needham  performed  a  number  of  experi- 
ments to  test  this  conclusion.  He  extracted  the  juices  of  meat  by 
boiling,  enclosed  them  in  bottles,  which  were  carefully  corked  and 
sealed  with  mastic,  then  subjected  the  closed  bottles  to  heat  and 
set  them  away  to  cool.  In  due  course  of  time,  the  fluids  thus  treated 
became  infected  with  microscopic  life,  and  inasmuch  as  he  believed 


474  Questions  and  Exercises 

that  he  had  killed  all  living  germs  by  repeated  heating,  he  concluded 
that  the  living  forms  had  been  produced  by  spontaneous  generation 
Spellanzani,  however,  thought  that  Needrram's  experiments  had 
not  been  conducted  with  sufficient  care.  He  therefore  made  a 
great  number  of  similar  experiments,  using  different  kinds  of  infu- 
sions. But  he  placed  them  in  thin  flasks  with  slender  necks,  which 
were  then  hermetically  sealed  in  flame,  after  which  he  immersed  the 
flasks  in  boiling  water  for  three  quarters  of  an  hour,  in  order  to  de- 
stroy all  germs  that  might  be  contained  in  them.  Under  these  con- 
ditions no  infusoria  appeared  in  them.  Needham  was  not  satisfied 
with  these  results,  however,  and  objected  that  such  a  prolonged  boil- 
ing would  destroy  not  only  germs,  but  the  germinative  force  of  the 
infusion  itself.  Spellanzani  easily  disposed  of  this  objection  by 
showing  that  when  the  infusions  were  again  exposed  to  the  air,  no 
matter  how  severe  or  prolonged  the  boiling  to  which  they  had  been 
subjected,  the  infusoria  reappeared.     (Ibid.) 

22.  These  and  similar  experiments  proved  that  there  is  some- 
thing in  the  atmosphere  which,  unless  it  be  removed  or  rendered 
inactive,  produces  life  within  nutrient  fluids,  but  whether  this 
something  is  solid,  fluid,  or  gaseous  did  not  appear  from  the  experi- 
ments. In  1843,  however,  Helmholtz  showed  that  this  something 
will  not  pass  through  a  moist  animal  membrane,  as  fluids  and  gases 
will.     (Ibid.) 

23.  In  the  '70's,  the  discussion  of  spontaneous  generation  having 
been  revived,  Tyndall  showed  that  in  an  hermetically  closed  box, 
within  which  the  air  was  what  he  called  'optically  pure, '  or  entirely 
free  from  all  floating  particles,  putrescible  liquids  in  test-tubes, 
previously  sterilized,  might  be  exposed  indefinitely  without  spoiling. 
But  on  admitting  the  outside  air  even  for  an  instant,  the  liquids 
within  a  few  days  were  spoiled  and  full  of  micro-organisms. 
(Ibid.) 

24.  Pouchet  devised  an  experiment  to  prove  the  spontaneous 
generation  of   micro-organisms,  in  which  an  hermetically  sealed 


Questions  and  Exercises  475 

vessel,  previously  filled  with  boiling  water,  was  opened  beneath  the 
surface  of  a  basin  of  mercury,  so  as  to  exclude  all  air,  and  some 
sterilized  hay  and  absolutely  pure  oxygen,  made  at  a  temperature 
of  incandescence,  introduced.    The  infusion  moulded. 

Pasteur  replied  to  this  by  showing  that  the  surface  of  the  mercury 
was  covered  with  minute  particles  of  atmospheric  dust.  (Vallery- 
Radot,  Louis  Pasteur.) 

25.  Pasteur  took  a  series  of  bulbs  of  about  a  quarter  of  a  litre  in 
capacity,  and  after  having  half-filled  them  with  a  putrescible  liquid, 
he  drew  out  the  necks  by  means  of  the  blowpipe,  then  caused  the 
liquid  to  boil  for  some  minutes,  and  during  the  ebullition,  while  the 
steam  issued  from  the  tapering  ends  of  the  bulbs,  he  sealed  them 
with  the  lamp.  Thus  prepared,  the  bulbs  were  easily  transported. 
As  they  were  empty  of  air,  that  which  they  originally  contained 
having  been  driven  off,  when  the  sealed  end  was  broken  off,  the  air 
rushed  into  the  tube,  carrying  with  it  all  the  germs  it  held  in  suspen- 
sion. Closing  the  tube  immediately  afterwards  with  a  flame,  and 
leaving  the  vessels  to  themselves,  it  was  easy  to  recognize  those 
in  which  a  change  occurred. 

Pasteur  opened  and  resealed  20  of  these  bulbs  in  the  country,  far 
from  all  habitations ;  20  more  in  the  Jura,  at  850  metres  above  sea- 
level;  and  20  more  in  the  Montanvert,  at  2000  metres.  In  the 
first  20,  there  were  8  bulbs  in  which  organisms  appeared ;  in  the 
second  20,  there  were  5;  and  in  the  third  20,  only  1.     (Ibid.) 

26.  'Whether  or  not  a  bad  theory  is  better  than  none  depends 
upon  circumstances.'  Examine  this  statement,  and  point  out 
what  are  some  of  the  circumstances  of  which  mention  is  made. 

27.  It  is  said  that  a  general  resemblance  of  the  hills  near  Ballarat 
in  Australia  to  the  Californian  hills  where  gold  had  been  found 
suggested  the  idea  of  digging  for  gold  at  Ballarat.     (Minto.) 

28.  There  are  no  great  nations  of  antiquity  but  have  fallen  to 
the  hand  of  time;  and  England  must  join  them  to  complete  the 
analogy  of  the  ages.     Like  them  she  has  grown  from  a  birth-time 


476  Questions  and  Exercises 

of  weakness  and  tutelage  to  a  day  of  manhood  and  supremacy, 
but  she  has  to  face  her  setting.  Everything  that  grows  must  also 
decay.     (Edinburgh,  1893.) 

29.  Goldscheider  proved  that  muscular  sensations  play  no  con- 
siderable part  in  our  consciousness  of  the  movements  of  our  limbs, 
by  having  his  arm  suspended  in  a  frame  and  moved  by  an  attend- 
ant. Under  these  circumstances,  where  no  work  devolved  on 
his  muscles,  he  found  that  he  could  distinguish  as  small  an  angular 
movement  of  the  arm  as  when  he  moved  and  supported  it  himself. 

30.  Goldscheider  also  proved  that  the  chief  source  of  move- 
ment-consciousness is  pressure  sensations  from  the  inner  surface 
of  the  joints,  by  having  his  arm  held  so  that  the  joint  surfaces 
were  pressed  more  closely  together,  and  finding  that  a  smaller 
movement  was  now  perceptible. 

31.  Wages  in  the  United  States  are  higher  than  in  England, 
because  the  former  country  is  a  republic  and  has  a  protective 
tariff. 

32.  It  does  not  follow  that  an  institution  is  good  because  a 
country  has  prospered  under  it,  nor  bad  because  a  country  in 
which  it  exists  is  not  prosperous.  It  does  not  even  follow  that 
institutions  to  be  found  in  all  prosperous  countries,  and  not  to  be 
found  in  backward  countries,  are  therefore  beneficial.  For  this 
at  various  times  might  confidently  have  been  asserted  of  slavery, 
of  polygamy,  of  aristocracy,  of  established  churches ;  and  it  may 
still  be  asserted  of  public  debts,  of  private  property  in  land,  of 
pauperism,  and  of  the  existence  of  distinctly  vicious  or  criminal 
classes.     (George.) 

7,$.  "No  Body  can  be  healthfull  without  Exercise,  neither 
Naturall  Body,  nor  Politique :  And  certainly,  to  a  Kingdome  or 
Estate,  a  Just  and  Honourable  Warre,  is  the  true  Exercise.  A 
Civill  Warre,  indeed,  is  like  the  Heat  of  a  feaver;  but  a  Forraine 
Warre,  is  like  the  Heat  of  Exercise,  and  serveth  to  keepe  the  Body 
in  Health."     (Bacon,  Essays.) 


Questions  and  Exercises  477 

34.  Explain  the  procedure  of  the  reductio  ad  absurdum  form 
o\  argument. 

35.  It  may  be  a  coincidence  merely;  but,  if  so,  it  is  remarkably 
strange  that  while  the  chloroform  has  not  changed,  while  the  con- 
stitutions of  the  patients  have  not  changed,  where  the  use  of  the 
inhaler  is  the  rule,  there  are  frequent  deaths  from  chloroform; 
whilst  in  Scotland  and  Ireland,  where  the  use  of  the  inhaler  is  the 
exception,  deaths  are  proportionally  rare. 

36.  We  should  think  it  a  sin  and  shame  if  a  great  steamer, 
dashing  across  the  ocean,  were  not  brought  to  a  stop  at  a  signal 
of  distress  from  the  mere  smack.  .  .  .  And  yet  a  miner  is  en- 
tombed alive,  a  painter  falls  from  a  scaffold,  a  brakeman  is  crushed 
in  coupling  cars,  a  merchant  fails,  falls  ill  and  dies,  and  organized 
society  leaves  widow  and  child  to  bitter  want  or  degrading  alms. 
(George,  Protection  and  Free  Trade.) 

37.  "  For  there  are  only  two  possible  a  priori  explanations  of 
adaptations  for  the  naturalist ;  namely,  the  transmission  of  func- 
tional adaptations  and  natural  selection;  but  as  the  first  of  these 
can  be  excluded,  only  the  second  remains."     (Weismann.) 

38.  The  planet  Mars  resembles  the  Earth  in  possessing  atmos- 
phere, water,  and  moderate  temperature,  and  we  may  therefore 
suppose  it  to  be  inhabited.     (St.  Andrews.) 

39.  Manufacturing  countries  are  always  rich  countries;  coun- 
tries that  produce  raw  material  are  always  poor.  Therefore,  if  we 
would  be  rich,  we  must  have  manufactures,  and  in  order  to  get 
them,  we  must  encourage  them.  .  .  .  But  I  could  make  as  good 
an  argument  to  the  little  town  of  Jamaica  ...  in  support  of  a 
subsidy  to  a  theatre,  I  could  say  to  them :  all  cities  have  theatres, 
and  the  more  theatres  it  has  the  larger  the  city.  Look  at  New 
York !  .  .  .  Philadelphia  ranks  next  to  New  York  in  the  number 
and  size  of  its  theatres,  and  therefore  comes  next  to  New  York  in 
wealth  and  population.  ...  I  might  then  drop  into  statistics 
.  .  .  and  point  to  the  fact  that  when  theatrical  representations 


478  Questions  and  Exercises 

began  in  this  country,  its  population  did  not  amount  to  a  million 
that  it  was  totally  destitute  of  railroads,  and  without  a  single  mile 
of  telegraph  wire.  Such  has  been  our  progress  since  theatres 
were  introduced  that  the  census  of  1880  showed  we  had  50,155,783 
people,  90,907  miles  of  railroad,  and  291,212^  miles  of  telegraph 
wires.     (George,   Protection  and  Free   Trade?) 

40.  What  methods  would  you  employ  to  investigate  the  connec- 
tion between  changes  in  the  barometer  and  in  the  weather? 

41.  In  Sir  Humphry  Davy's  experiments  upon  the  decompo- 
sition of  water  by  galvanism,  it  was  found  that,  besides  the  two 
components  of  water,  oxygen  and  hydrogen,  an  acid  and  an  alkali 
were  developed  at  the  two  opposite  poles  of  the  machine.  The 
insight  of  Davy  conjectured  that  there  might  be  some  hidden 
cause  of  this  portion  of  the  effect:  the  glass  containing  the  water 
might  suffer  partial  decomposition,  or  some  foreign  matter  might 
be  mingled  with  the  water,  and  the  acid  and  alkali  be  disengaged 
from  it,  so  that  the  water  would  have  no  share  in  their  production. 
...  By  the  substitution  of  gold  vessels  for  glass,  without  any 
change  in  the  effect,  he  at  once  determined  that  the  glass  was  not 
the  cause.  Employing  distilled  water,  he  found  a  marked  diminu- 
tion of  the  quantity  of  acid  and  alkali  evolved ;  yet  there  was 
enough  to  show  that  the  cause,  whatever  it  was,  was  still  in  opera- 
tion. ...  He  now  conceived  that  the  perspiration  from  the 
hands  touching  the  instruments  might  affect  the  case,  as  it  would 
contain  common  salt,  and  an  acid  and  an  alkali  would  result  from 
its  decomposition  under  the  agency  of  electricity.  By  caremlly 
avoiding  such  contact,  he  reduced  the  quantity  of  the  products 
still  further  until  no  more  than  slight  traces  of  them  were  percep- 
tible. What  remained  of  the  effect  might  be  traceable  to  im- 
purities of  the  atmosphere,  decomposed  by  contact  with  the 
electrical  apparatus.  An  experiment  determined  this:  the  machine 
was  put  under  an  exhausted  receiver,  and,  when  thus  secured  from 
atmospheric  influence,  it  no  longer  evolved  the  acid  and  the  alkali. 
(Gore,  The  Art  of  Scientific  Discovery.) 


Questions  and  Exercises  479 

42.  In  the  vast  majority  of  cases  the  best  brain  work  of  which  in- 
dividuals of  average  or  of  unusual  ability  are  capable  is  performed 
under  conditions  of  imperfect  health.  .  .  .  The  mind  at  its  best  is 
to  be  found  in  a  body  that  is  not  at  its  best.  ...  I  do  not  think 
it  can  be  doubted  that  as  classes,  country  clergymen,  army  men,  and 
country  gentlemen  enjoy  a  ruder  health  and  have  a  less  frequent 
resort  to  doctors  and  drugs  than  barristers,  journalists,  and  medical 
men.  The  natural  conditions  of  their  lives  .  .  .  and  their  open- 
air  habits  .  .  .  conduce  to  perfect  health.  I  do  not  think  it  can  be 
doubted,  that  as  classes,  clergymen,  army  men,  and  country  gentle- 
men are  characterized  by  brains  less  active  in  their  higher  intellectual 
functions  than  the  brains  of  the  less  healthy  professional  classes.  .  .  . 
The  case  for  my  proposition  becomes  even  stronger  when  preem- 
inent brain  work  is  considered.  I  cannot,  at  the  present  moment, 
recall  a  single  great  poet,  man  of  letters  or  man  of  science,  in  fact, 
any  person  greatly  distinguished  by  the  product  of  his  brain,  who 
was  a  type  of  good  health.  Examples  to  the  contrary  surge  into  the 
mind.  .  .  .  Consider  Newton,  always  an  invalid;  Clerk  Maxwell, 
who  died  young  after  a  life  of  ill-health;  Darwin,  who  after  he 
reached  adult  life  was  probably  never  well  for  three  consecutive 
days.  Consider  Poe  and  Pope,  Chatterton,  Keats,  Shelley,  Byron, 
Heine,  and  a  thousand  other  poets.  Consider  Gibbon  and  Carlyle, 
De  Quincey  —  it  is  needless  to  prolong  the  catalogue;  but  I  would 
ask  readers  to  think  over  the  distinguished  people  they  know.  It 
is  difficult  to  mention  the  names  of  living  distinguished  persons, 
but  for  my  own  part  I  am  certain  that  I  do  not  know  a  single  per- 
son whose  intellect  I  respect  greatly,  who  enjoys  robust  health. 
(Saturday  Review.) 

43.  It  was  formerly  supposed  that  all  the  nervous  fibres  in  the 
body  exercised  both  the  function  of  conveying  motor  stimuli  to  the 
muscles,  and  sensory  stimuli  to  the  brain.  This  was  apparently 
confirmed  by  the  fact  that  when  any  nerve  was  severed  both  sensation 
and  motion  disappeared  in  the  part  to  which  it  led.  But  in  181 1, 
Sir  Charles  Bell  published  an  essay  to  show  that  nerves  were  com- 


480  Questions  and  Exercises 

posed  of  various  filaments,  whose  function  differed  according  to  th« 
location  of  their  original  roots  in  the  brain  or  in  the  spinal  cord. 
This  theory,  he  pointed  out,  would  account  for  the  extreme  com- 
plexity of  <he  structure  of  the  brain  and  of  the  nervous  system, 
which  on  the  older  supposition  remained  entirely  unexplained.  It 
was  absurd,  he  also  maintained,  to  suppose  that  one  and  the  same 
nerve-fibre  could  conduct  sensory  stimuli  to  the  brain  and  motor 
stimuli  from  it  at  the  same  instant ;  yet  we  are  constantly  moving 
a  part  at  the  same  time  that  we  receive  sensations  from  it. 

44.  In  order  to  experimentally  test  his  theory,  he  selected  two 
of  the  cerebral  nerves,  the  portio  dura  and  the  fifth  pair,  the  first  of 
which  has  one  root,  while  the  latter  has  two.  On  cutting  the  portio 
dura  in  a  living  animal,  motion  only  was  lost  in  the  parts  with  which 
it  communicates.  The  fifth  pair  has  some  branches  which  arise 
from  only  one  of  its  roots,  and  some  which  arise  from  both  roots. 
On  cutting  the  first  set  of  branches,  sensation  only  disappeared, 
on  cutting  the  second,  both  sensation  and  the  power  of  motion  were 
destroyed. 

45.  The  spinal  nerves  have  two  roots,  an  anterior  and  a  posterior. 
When  Bell  exposed  and  irritated  the  anterior  root,  convulsive  move- 
ments of  the  muscles  were  set  up ;  but  on  irritating  the  posterior 
root,  no  movement  followed.  He  felt  assured,  therefore,  that  the 
motor  function  was  confined  to  the  fibres  of  the  anterior  root; 
but  inasmuch  as  the  operation  of  exposing  the  roots  was  intensely 
painful  to  the  animal,  he  could  not  be  certain  that  sensation  was  set 
up  by  the  fibres  of  the  posterior  root  only. 

46.  It  was  pointed  out,  however,  that  in  some  cases  of  partial 
paralysis  of  the  limbs  with  which  these  nerves  communicate,  motion 
alone  is  lost,  while  the  power  of  sensation  is  retained ;  in  other  cases, 
the  reverse  condition  obtains.  This  seems  to  show  —  (What?  and 
How?) 

47.  Glaciers  are  ice-streams,  or  rivers  in  which  the  moving  mate- 
rial is  frozen  instead  of  liquid  water.      Like  large  rivers,  they  ordi 


Questions  mid  Exercises  481 

narily  have  their  sources  in  high  mountains,  and  descend  along  the 
valleys ;  but  the  mountains  are  such  as  to  take  snow  from  the  clouds 
instead  of  rain,  because  of  their  elevation.  Like  large  rivers,  many 
tributary  streams  coming  from  the  different  valleys  unite  to  make 
the  great  stream.  As  with  rivers,  their  movement  is  dependent  on 
gravity,  or  the  weight  of  the  material ;  but  the  average  rate  of  motion, 
instead  of  being  several  miles  an  hour,  is  generally  in  summer  but 
10  to  18  inches  a  day,  or  a  mile  in  18  to  20  years.  As  with  rivers, 
the  central  portions  move  most  rapidly,  the  sides  and  bottom  being 
retarded  by  friction.     (J.  D.  Dana.) 

48.  The  human  race,  Mr.  Fries  contends,  suffers  no  ill-effects 
from  its  meat-eating  habits.  Yet  it  is  generally  acknowledged  that 
the  human  race  dies  very  prematurely,  —  so  prematurely,  in  fact, 
that  a  full  third  of  people's  lives  is  cut  off  entirely.  It  is  generally 
recognized  by  biologists  that  any  animal  should  live  five  times  the 
length  of  its  period  of  maturity;  a  dog  matures  at  2  and  dies  at  10, 
etc.  This  is  the  average  that  maybe  observed  throughout  the  animal 
kingdom.  Man,  it  is  asserted,  matures  at  about  25,  so  that,  by  anal- 
ogy, he  should  live  to  be  125  years  old  —  and  that  before  he  shows 
signs  of  decrepitude,  mental  or  physical.  Yet,  in  place  of  this, 
what  do  we  find  ?  That  the  average  term  of  life  is  something  over  42 
years,  and,  not  only  that,  but  those  42  years  are  filled  with  sick- 
nesses and  diseases  of  all  kinds,  as  human  experience  testifies.  Is 
this  a  normal  condition?  Or  is  there  not  something  wrong  some- 
where to  produce  these  results;  and  what  so  wrong  and  per- 
verted as  the  present  food  habits  of  the  people?  (Letter  to 
N.  Y.  Times.) 

49.  (a)  Moisture  bedews  a  cold  metal  or  stone  when  we  breathe 
on  it.  The  same  appears  on  a  glass  of  ice-water,  and  on  the  in- 
side of  windows  when  sudden  rain  or  hail  chills  the  external  air. 
The  inference  is  that  when  an  object  contracts  dew  it  is  colder 
than  the  surrounding  air. 

(b)  No  dew  is  deposited  on  a  piece  of  polished  metal,  but  on 
2  1 


482  Questions  and  Exercises 

the  same  metal  unpolished  dew  is  deposited  copiously.  There- 
fore the  deposit  of  dew  is  affected  by  the  kinds  of  surface  exposed. 

{c)  With  various  kinds  of  polished  metals,  no  dew  is  deposited ; 
but  with  various  kinds  of  highly  polished  glass  dew  is  deposited. 
Therefore  the  deposit  of  dew  is  affected  by  the  kinds  of  substances 
exposed. 

(d)  It  is  known  by  direct  experiment  that  for  any  given  degree 
of  temperature,  only  a  limited  amount  of  water  can  remain  sus- 
pended as  vapour,  and  this  quantity  grows  less  and  less  as  the  tem- 
perature diminishes.  Therefore  if  there  is  already  as  much  vapour 
suspended  as  the  air  will  contain  at  its  existing  temperature,  any 
lowering  of  the  temperature  will  cause  necessarily  a  portion  of  the 
vapour  to  be  condensed  as  dew.     (Hibben.) 

50.  Properties  known  to  exist  in  potassium  have  been  predicted 
of  and  found  to  exist  in  rubidium ;  for  instance,  the  carbonates  of 
sodium  and  potassium  are  not  decomposed  by  a  red  heat,  neither 
are  those  of  rubidium,  or  caesium.  Some  of  the  statements  which 
are  true  of  chlorine  have  been  found  to  be  true,  in  varying  degrees, 
of  bromine  and  iodine.  .  .  .  After  I  had  found  the  molecular 
change  in  antimony  electro-deposited  from  its  chloride,  I  sought 
for  and  discovered  it  in  that  deposited  from  its  bromide  and  iodide ; 
and  after  having  found  magnetic  changes  in  iron  by  heat,  I  also 
found  similar  ones  in  nickel.  (Gore,  The  Art  0/ Scientific  Dis- 
covery.) 

51.  What  inductive  fallacy  may  David  be  said  to  have  com- 
mitted when,  he  said  in  his  haste  that  all  men  are  liars  ? 

52.  It  has  been  found  that  linnets  when  shut  up  and  educated 
with  singing  larks  —  the  skylark,  woodlark,  or  titlark  —  will 
adhere  entirely  to  the  songs  of  these  larks,  instead  of  the  natural 
song  of  the  linnets.  We  may  infer,  therefore,  that  birds  learn  to 
sing  by  imitation,  and  that  their  songs  are  no  more  innate  than 
language  is  in  man.     (Hyslop.) 

53.  We  observe  very   frequently  that   very  poor   handwriting 


Questions  and  Exercises  483 

characterizes  the  manuscripts  of  able  men,  while  the  best  hand 
writing  is  as  frequent  with  those  who  do  little  mental  work  when 
compared  with  those  whose  penmanship  is  poor.  We  may, 
therefore,  infer  that  poor  penmanship  is  caused  by  the  influence 
of  severe  mental  labour.     (Hyslop.) 

54.  Galileo  describes  his  invention  of  the  telescope  as  follows: 
This  then  was  my  reasoning;  this  instrument  [of  which  he  had 
heard  a  rumour]  must  either  consist  of  one  glass,  or  of  more  than 
one;  it  cannot  be  of  one  alone,  because  its  figure  must  be  either 
concave  or  convex,  or  comprised  within  two  parallel  superficies, 
but  neither  of  these  shapes  alter  in  the  least  the  objects  seen, 
although  increasing  or  diminishing  them;  for  it  is  true  that  the 
concave  glass  diminishes,  and  that  the  convex  glass  increases 
them ;  but  both  show  them  very  indistinctly,  and  hence  one  glass 
is  not  sufficient  to  produce  the  effect.  Passing  on  to  two  glasses, 
and  knowing  that  the  glass  of  parallel  superficies  has  no  effect  at 
all,  I  concluded  that  the  desired  result  could  not  possibly  follow 
by  adding  this  one  to  the  other  two.  I  therefore  restricted  my 
experiments  to  combinations  of  the  other  two  glasses;  and  I  saw 
how  this  brought  me  to  the  result  I  desired.  (Quoted  by  Gore, 
The  Art  of  Scientific  Discovery.) 

55.  Darwin  was  struck  by  the  number  of  insects  caught  by  the 
leaves  of  the  common  sun-dew.  It  soon  became  evident  to  him 
that  "Drosera  was  excellently  adapted  for  the  special  purpose  of 
catching  insects."  ...  As  soon  as  he  began  to  work  on  Drosera, 
and  was  led  to  believe  that  the  leaves  absorbed  nutritious  matter 
from  the  insects,  he  began  to  reason  by  analogy  from  the  well-un- 
derstood digestive  capacity  of  animals.  ...  Having  by  analogy 
established  the  power  of  digestion  in  plants,  analogy  led  him  to 
seek  in  plants  the  elements  that  do  the  work  of  digestion  in  animals. 
Bringing  together  what  was  known  of  plants,  he  pointed  out  that 
the  juices  of  many  plants  contain  an  acid,  and  so  one  element  of  a 
digestive  fluid  was  at  hand;  and  that  all  plants  possess  the  pcwer 


484  Questions  and  Exercises 

of  dissolving  albuminous  or  proteid  substances,  protoplasm,  chlo 
rophyl,  etc.,  and  that  "this  must  be  effected  by  a  solvent,  proba- 
bly consisting  of  a  ferment  together  with  an  acid."  After  writing 
the  last-quoted  sentence,  he  learned  that  a  ferment  which  con- 
verted albuminous  substances  into  true  peptones  had  been  ex- 
tracted from  the  seeds  of  the  vetch.  (Cramer,  The  Method  of 
Darwin.) 

56.  Strongly  impressed  with  the  belief  that  some  "  harmonic  " 
relation  must  exist  among  the  distances  of  the  several  planets 
from  the  sun,  and  also  among  the  times  of  their  revolution,  Kepler 
passed  a  large  part  of  his  early  life  in  working  out  a  series  of  guesses 
at  this  relation,  some  of  which  now  strike  us  as  not  merely  most 
improbable,  but  positively  ridiculous.  His  single-minded  devo- 
tion to  truth,  however,  led  him  to  abandon  each  of  these  hypotheses 
in  turn  so  soon  as  he  perceived  its  fallacy  by  submitting  it  to  the 
test  of  its  conformity  to  observed  facts.  .  .  .  But  he  was  at  last 
rewarded  by  the  discovery  of  that  relation  between  the  times  and 
the  distances  of  the  planetary  revolutions,  which  with  the  dis- 
covery of  the  ellipticity  of  the  orbits,  and  of  the  passage  of  the 
radius  vector  over  equal  areas  in  equal  times  has  given  him  immor- 
tality as  an  astronomical  discoverer.  But  ...  he  was  so  far 
from  divining  the  true  rationale  of  the  planetary  revolutions  that 
he  was  led  to  the  discovery  of  the  elliptical  orbit  of  Mars  by  a 
series  of  happy  accidents  .  .  .  whilst  his  discovery  of  the  true 
relations  of  times  and  distances  was  the  fortunate  guess  which  closed 
a  long  series  of  unfortunate  ones,  many  of  which  were  no  less 
ingenious. 

Now  it  was  by  a  grand  effort  of  Newton's  constructive  imagina- 
tion, based  on  his  wonderful  mastery  of  geometrical  reasoning, 
that,  starting  with  the  conception  of  two  forces,  one  of  them  tend- 
ing to  produce  continuous  uniform  motion  in  a  straight  line,  the 
other  tending  to  produce  a  uniformly  accelerated  motion  towards 
a  fixed  point,  he  was  able  to  show  that  if  these  dynamical  assump- 


Questions  and  Exercises  485 

tions  were  granted,  Kepler's  laws,  being  consequences  of  them, 
must  be  universally  true.  And  it  was  his  still  greater  glory  to 
divine  the  profound  truth  that  the  fall  of  the  moon  towards  the 
earth  —  that  is,  the  deflection  of  her  path  from  a  tangential  line  to 
an  ellipse  —  is  a  phenomenon  of  the  same  order  as  the  fall  of  a  stone 
to  the  ground.     (Gore,  The  Art  of  Scientific  Discovery.) 

57.  After  Franklin  had  investigated  the  nature  of  electricity 
for  some  time,  he  began  to  consider  how  many  of  the  effects  of 
thunder  and  lightning  were  the  same  as  those  produced  by  elec- 
tricity. Lightning  travels  in  a  zigzag  line,  and  so  does  an  electric 
spark;  electricity  sets  things  on  fire,  so  does  lightning;  electricity 
melts  metals,  so  does  lightning.  Animals  can  be  killed  by  both, 
and  both  cause  blindness.  Pointed  bodies  attract  the  electric 
spark,  and  in  the  same  way  lightning  strikes  spires,  and  trees,  and 
mountain  tops.  Is  it  not  likely  then  that  lightning  is  nothing 
more  than  electricity  passing  from  one  cloud  to  another,  just  as  an 
electric  spark  passes  from  one  substance  to  another  ?  (Buckley, 
A  Short  History  of  Natural  Science.) 

58.  How  did  Franklin  proceed  to  verify  the  hypothesis  stated 
in  the  last  example? 

59.  When  men  had  formed  a  notion  of  the  moon  as  a  solid  body 
revolving  about  the  earth,  they  had  only  further  to  conceive  it 
spherical,  and  to  suppose  the  sun  to  be  beyond  the  region  of  the 
moon,  and  they  would  find  that  they  had  obtained  an  explanation 
of  the  varying  forms  which  the  bright  part  of  the  moon  assumes  in 
the  course  of  a  month.  For  the  convex  side  of  the  crescent-moon, 
and  her  full  edge  when  she  is  gibbous,  are  always  turned  towards 
the  sun.  And  this  explanation,  once  suggested,  would  be  confirmed 
the  more  it  was  examined.  For  instance,  if  there  be  near  us  a 
spherical  stone,  on  which  the  sun  is  shining,  and  if  we  place  ourselves 
so  that  this  stone  and  the  moon  are  seen  in  the  same  direction  (the 
moon  appearing  just  over  the  top  of  the  stone),  we  shall  find  that 
the  visible  part  of  the  stone,  which  is  then  illuminated  by  the  sun, 


4$6  Questions  and  Exercises 

is  exactly  similar  in  form  to  the  moon,  at  whatever  period  of  hel 
changes  she  may  be.     (Whewell.) 

60.  Not  long  ago  the  adherents  of  spontaneous  generation  urged 
as  an  argument  on  their  side  that  if  biogenesis  be  true,  innumerable 
facts  and  experiments  prove  that  the  air  must  be  thick  with  germs, 
and  they  regarded  this  as  the  height  of  absurdity.  But  that  micro- 
organisms exist  everywhere  has  since  been  shown  beyond  the 
shadow  of  a  doubt. 

61.  In  every  animal  possessing  a  circulation  of  the  blood  which 
had  been  observed  up  to  1824,  the  current  of  the  blood  was  known  to 
take  one  definite  and  invariable  direction.  Now,  there  is  a  class  of 
animals  called  Ascidians  which  possess  a  heart  and  a  circulation, 
and  up  to  this  period  no  one  would  have  dreamt  of  questioning  the 
propriety  of  the  deduction  that  these  creatures  have  a  circulation 
in  one  direction ;  nor  would  any  one  have  thought  it  worth  while  to 
verify  the  point.  But  in  that  year  M.  von  Hasselt,  happening  to 
examine  a  transparent  animal  of  this  class,  found  to  his  infinite 
surprise  that  after  the  heart  had  beat  a  certain  number  of  times,  it 
stopped,  and  then  began  beating  the  opposite  way  —  so  as  to  re- 
verse the  course  of  the  current,  which  returned  by  and  by  to  its 
original  direction.     (Huxley.) 

62.  "Sir  Oliver  Lodge  ...  is  persuaded  that  messages  are 
received  from  the  dead.  ...  Sir  Oliver  .  .  .  seems  an  easy 
man  to  convince.  The  message  ■ — ■  through  the  usual  medium  — 
is  presumably  from  Frederic  W.  H.  Myers.  ...  In  his  lifetime 
he  was  an  essayist  and  poet  of  unusual  delicacy  of  taste  and  pre- 
cision of  style.  ...  It  is  painful,  therefore,  to  ascribe  to  Mr. 
Myers  these  lines:  — 

Friend,  while  on  earth  with  knowledge  slight, 
I  had  the  living  power  to  write ; 
Death  tutored  now  in  things  of  might, 
I  yearn  to  you  and  cannot  write. 

And  this  from  a  man  'of  rare  intellectual  gifts,  original,  acute, 
and  thoughtful'  1 "     {Nation.) 


Questions  and  Exercises  487 

63.  Sir  Oliver  Lodge  replied  that  "It  would  be  painful  toatrrib 
ute  (this  passage)  to  the  developed  intelligence  of  Mr.  Myers  ot 
any  other  poet.  But  in  what  evidence  do  you  assume  that  we  have 
done  so  ?  Ought  a  schoolboy  exercise  in  a  foreign  language  or 
a  rhyme  constructed  between  sleep  and  waking  to  be  esteemed  part 
of  the  output  of  a  man  of  letters?  "     (Letter  to  Nation.) 

64.  The  following  is  the  cardinal  passage  in  Harvey's  famous 
argument  for  the  circulation  of  the  blood:  "Let  us  assume  either 
arbitrarily  or  from  experiment,  the  quantity  of  blood  which  the 
left  ventricle  of  the  heart  will  contain  when  distended,  to  be,  say, 
two  ounces,  three  ounces,  or  one  ounce  and  a  half  —  in  the  dead 
body  I  have  found  it  to  hold  upwards  of  two  ounces.  .  .  .  Let  us 
suppose  as  approaching  the  truth  that  the  fourth,  or  fifth,  or  sixth, 
or  even  that  the  eighth  part  of  its  charge  is  thrown  into  the  artery 
at  each  contraction ;  this  would  give  either  half  an  ounce,  or  three 
drachms,  or  one  drachm  of  blood  as  propelled  by  the  heart  at  each 
pulse  into  the  aorta;  which  quantity,  by  reason  of  the  valves  at 
the  root  of  the  vessel,  can  by  no  means  return  into  the  ventricle. 
Now,  in  the  course  of  half  an  hour,  the  heart  will  have  made 
more  than  one  thousand  beats,  in  some  as  many  as  two,  three, 
and  even  four  thousand.  Multiplying  the  number  of  drachms 
propelled  by  the  number  of  pulses,  we  shall  have  either  one  thou- 
sand half  ounces,  or  one  thousand  times  three  drachms,  or  a  like 
proportional  quantity  of  blood,  according  to  the  amount  which 
we  assume  as  propelled  with  each  stroke  of  the  heart,  sent  from 
this  organ  into  the  artery;  a  larger  quantity  in  every  case  than  is 
contained  in  the  whole  body!  .  .  .  (Thus),  supposing  even  the 
smallest  quantity  of  blood  to  be  passed  through  the  heart  and  the 
lungs  with  each  pulsation,  a  vastly  greater  amount  would  still  be 
thrown  into  the  arteries  .  .  .  than  could  by  any  possibility  be  sup- 
plied by  the  food  consumed.  It  could  be  furnished  in  no  other 
way  than  by  making  a  circuit  and  returning."  (De  motu  cordis, 
Ch.  IX.) 


488  Questions  and  Exercises 

65.  The  older  theory  was  that  the  arterial  pulse  served  the  same 
purpose  as  respiration.  One  of  Harvey's  arguments  against  this 
is  as  follows;  "Now  if  the  arteries  are  filled  in  the  diastole  with 
air  then  taken  into  them  (a  larger  quantity  of  air  penetrating  when 
the  pulse  is  strong  and  full),  it  must  come  to  pass,  that  if  you  plunge 
into  a  bath  of  water  or  oil  when  the  pulse  is  strong  and  full,  it  ought 
forthwith  to  become  either  smaller  or  much  slower,  since  the  cir- 
cumambient bath  will  render  it  either  difficult  or  impossible  for 
the  air  to  penetrate." 

66.  Galileo  discovered  by  means  of  his  telescope  that  Jupiter 
has  four  moons,  instead  of  one  like  the  earth,  and  he  regarded 
this  discovery  as  a  confirmation  of  the  Copernican  theory.  Ex- 
plain the  nature  of  the  reasoning  involved  in  reaching  this  con- 
clusion. 

67.  That  the  period  of  tide  should  be  accidentally  the  same  as 
that  of  the  culmination  of  the  moon,  that  the  period  of  the  highest 
tide  should  be  accidentally  the  same  as  the  syzygies,  is  possible 
in  abstracto;  but  it  is  in  the  highest  degree  improbable:  the  far 
more  probable  assumption  is,  either  that  the  sun  and  moon  pro- 
duce the  tide,  or  that  their  motion  is  due  to  the  same  grounds  as 
the  motion  of  the  tide.     (Hibben.) 

68.  During  the  retreat  of  the  Ten  Thousand  a  cutting  north 
wind  blew  in  the  faces  of  the  soldiers ;  sacrifices  were  offered  to 
Boreas,  and  the  severity  of  the  wind  immediately  ceased,  which 
seemed  a  proof  of  the  god's  causation.     {Anabasis,  Bk.  IV.) 

69.  A  nectary  implies  nectar,  but  Sprengel  had  come  to  the 
conclusion  that  orchis  morio  and  orchis  maculata,  though  furnished 
with  nectaries,  did  not  secrete  nectar.  Darwin  examined  the 
flowers  of  orchis  morio  for  twenty-three  consecutive  days,  looking 
at  them  after  hot  sunshine,  after  rain,  and  at  all  hours;  he  kept 
the  spikes  in  water  and  examined  them  at  midnight  and  early  the 
next  morning.  He  irritated  the  nectaries  with  bristles,  and  ex- 
posed them  to  irritating  vapours.     He  examined  flowers  whose 


Questions  and  Exercises  489 

pollinia  had  been  removed,  and  others  which  would  probably 
have  them  soon  removed.  But  the  nectary  was  invariably  dry. 
He  was  thoroughly  convinced,  however,  that  these  orchids 
require  the  visits  of  insects  for  fertilization,  and  that  insects  visit 
flowers  for  the  attractions  offered  in  the  way  of  nectar,  and  yet 
that  in  these  orchids  the  ordinary  attraction  was  absent.  In 
examining  the  orchids  he  was  surprised  at  the  degree  to  which 
the  inner  and  outer  membranes  forming  the  tube  or  spur  were 
separated  from  each  other,  also  at  the  delicate  nature  of  the  inner 
membrane,  and  the  quantity  of  fluid  contained  between  the  two 
membranes.  He  then  examined  other  forms  that  do  secrete 
nectar  in  the  ordinary  way,  and  found  the  membranes  closely 
united,  instead  of  separated  by  a  space.  "I  was  therefore  led  to 
conclude,"  he  says,  "that  insects  penetrate  the  lax  membrane  of 
the  nectaries  of  the  above-named  orchids  and  suck  the  copious 
fluid  between  the  two  membranes."  He  afterwards  learned  that 
at  the  Cape  of  Good  Hope  moths  and  butterflies  penetrate  peaches 
and  plums,  and  in  Queensland  a  moth  penetrates  the  rind  of  the 
orange.  These  facts  merely  proved  his  anticipation  less  anoma- 
lous than  it  had  seemed.     (Cramer,  The  Method  of  Darwin?) 

70.  Construct  an  hypothesis  to  explain  some  fact  of  your  expe- 
rience, and  explain  how  it  may  be  either  verified  or  overthrown. 

71.  When  Darwin  began  to  work  on  Drosera  he  was  led  to 
believe  that  the  leaves  absorbed  nutritious  matter  from  insects. 
He  then  reasoned  by  analogy  from  the  well-understood  digestive 
capacity  of  animals.  He  made  preliminary  'crucial '  experiments 
by  immersing  some  leaves  of  Drosera  in  nitrogenous  and  others 
in  non-nitrogenous  fluids  of  the  same  density  to  determine 
whether  the  former  affected  the  leaves  differently  from  the  latter. 
This  he  found  to  be  the  case.  He  then  experimented  with  solid 
animal  matter  and  found  that  the  leaves  are  capable  of  true  diges- 
tion. Analogy  then  led  him  to  seek  in  plants  the  elements  that  do 
the  work  of  digestion  in  animals.     He  pointed  out  that  the  juices 


49°  Questions  and  Exercises 

of  many  plants  contain  an  acid,  and  so  one  element  of  a  digestive 
fluid  was  at  hand;  and  that  all  plants  possess  the  power  of  dis- 
solving albuminous  or  proteid  substances,  protoplasm,  chlorophyl, 
and  that  this  must  be  effected  by  a  solvent  consisting  probably 
of  a  ferment  together  with  an  acid.  Afterwards  he  learned  that 
a  ferment  which  converted  albuminous  substances  into  true  pep- 
tones had  been  extracted  from  the  seeds  of  the  vetch.  (Cramer, 
The  Method  of  Darwin,  pp.  95-99.) 

72.  In  opposition  to  the  facts  stated  above,  Tischutkin  main- 
tains that  the  'digestion'  of  insectivorous  plants  is  not  accom- 
plished in  the  same  way  as  in  animals,  but  is  due  to  bacteria :  that 
the  pepsin  is  not  a  secretion  of  the  plant,  but  a  by-product  of  the 
activity  of  the  bacteria.  Suppose  that  this  theory  is  true,  and 
Darwin's  false,  what  would  you  say  regarding  the  character  of  the 
latter's  reasoning  ? 

73.  Vesalius,  the  founder  of  modern  anatomy,  found  that  the 
human  thigh  bone  was  straight,  and  not  curved,  as  Galen,  the 
great  authority  on  the  subject  for  over  a  thousand  years,  had 
asserted.  Sylvius  replied  that  Galen  must  be  right;  that  the  bone 
was  curved  in  its  natural  condition,  but  that  the  narrow  trousers 
worn  at  the  time  had  made  it  artificially  straight. 

74.  "  From  looking  at  species  as  only  strongly-marked  and 
well-defined  varieties,  I  was  led  to  anticipate  that  the  species  of 
the  larger  genera  in  each  country  would  oftener  present  varieties 
than  the  species  of  the  smaller  genera;  for  wherever  many 
closely  related  species  {i.e.  species  of  the  same  genus)  have  been 
formed  many  varieties  or  incipient  species  ought,  as  a  general  rule 
to  be  now  forming.  ...  To  test  the  truth  of  this  anticipation  I 
have  arranged  the  plants  of  twelve  countries,  and  the  coleopterous 
insects  of  two  districts  into  two  nearly  equal  masses,  the  species  of 
the  larger  genera  on  one  side  and  those  of  the  smaller  genera  on  the 
other  side,  and  it  has  invariably  proved  to  be  the  case  that  a  larger 
proportion  of  the  species  on  the  side  of  the  larger  genera  presented 


Questions  and  Exercises  491 

varieties  than  on  the  side  of  the  smaller  genera.  Moreover,  the 
species  of  the  large  genera  which  present  any  varieties  invariably 
present  a  larger  average  number  of  varieties  than  do  the  species  of 
the  small  genera.  Both  of  these  results  follow  when  another  di- 
vision is  made,  and  when  all  the  least  genera  with  only  one  to  four 
species  are  altogether  excluded  from  the  tables. "  (Darwin,  Origin 
of  Species.) 

75.  Sir  Joseph  Lister,  the  founder  of  aseptic  surgery,  states  the 
origin  of  his  method  as  follows:  "When  it  had  been  shown  by  the 
researches  of  Pasteur  that  the  septic  property  of  the  atmosphere  de- 
pended, not  on  oxygen  or  any  gaseous  constituent,  but  on  minute 
organisms  suspended  in  it,  which  owed  their  energy  to  their  vitality, 
it  occurred  to  me  that  decomposition  in  the  injured  part  might  be 
avoided  without  excluding  the  air,  by  applying  as  a  dressing  some 
material  capable  of  destroying  the  life  of  the  floating  particles." 
At  first  he  used  carbolic  acid  for  this  purpose.  T  he  wards  of  which 
he  had  charge  in  the  Glasgow  Infirmary  were  especially  affected  by 
gangrene,  but  in  a  short  time  became  the  healthiest  in  the  world; 
while  other  wards  separated  only  by  a  passageway  retained  their 
infection.     (Locy.) 

76.  The  spectroscope.  .  .  has  suggested  the  presence  of  sub- 
stances not  known  upon  the  earth .  To  one  of  these  substances,  indi- 
cated by  a  green  line  in  the  spectrum  of  the  sun's  corona,  the  name 
Coronium  has  been  given  provisionally.  It  has  been  suggested  that 
this  line  may  represent  not  a  new  substance,  but  known  substances 
under  the  unknown  conditions  of  the  sun's  temperature.  However, 
as  it  exists  at  least  300,000  miles  from  the  sun,  it  is  impossible  that 
the  conditions  of  temperature  are  so  entirely  different  from  those 
known  to  us  as  completely  to  disguise  known  substances,  and  most 
scientists  now  accept  the  conclusion  that  the  green  line  is  caused  by 
the  presence  of  an  element  hitherto  unknown  in  any  other  region  of 
nature.  Recently,  Professor  Nasini  of  Padua,  with  two  colleagues, 
has  been  examining  the  gases  of  the  volcanic  regions  of  his  country 


492  Questions  and  Exercises 

.  .  .  for  argon  and  helium  (and  in  them)  he  has  discovered  the 
existence  of  coronium.     {Saturday  Review.) 

77.  It  was  discovered  by  Arago  in  181 1,  and  by  Biot  in  1812 
and  1818,  that  a  plate  of  rock-crystal,  cut  perpendicular  to  the 
axis  of  the  prism,  possessed  the  power  of  rotating  the  plane  of  polar- 
ization through  an  angle,  dependent  on  the  thickness  of  the  plane 
and  the  refrangibility  of  the  light.  It  was,  moreover,  proved  by 
Biot  that  there  existed  two  species  of  rock-crystal,  one  of  which 
turned  the  plane  of  polarization  to  the  right,  and  the  other  to  the  left. 
No  external  difference  of  crystalline  form  was  at  first  noticed  which 
could  furnish  a  clew  to  this  difference  of  action.  But  closer  scrutiny 
revealed  upon  the  crystals  minute  facets,  which,  in  the  one  class, 
were  ranged  along  a  right-handed,  and,  in  the  other,  along  a  left- 
handed  spiral,  thus  making  the  crystals  dissymmetrical  in  opposite 
ways.     (Tyndall,  in  Vallery-Radot,  Louis  Pasteur.) 

78.  Mitscherlich  brought  forward  the  tartrates  and  paratartrates 
of  ammonia  and  soda,  and  affirmed  them  to  possess  the  same 
chemical  constitution,  and  the  same  outward  crystalline  form,  the 
tartrates,  nevertheless,  causing  the  plane  of  polarization  to  rotate 
while  the  paratartrates  did  not.  It  seemed  to  Pasteur  that  there 
was  a  profound  incompatibility  between  the  identity  affirmed  by 
Mitscherlich  and  this  discrepancy  of  optic  character.  Remember- 
ing, no  doubt,  the  observations  of  Biot,  he  instituted  a  search  for 
facets  like  those  discovered  in  rock-crystal,  and  which,  without 
altering  chemical  constitution,  destroyed  crystalline  identity.  He 
found  that  the  crystalline  forms  of  tartaric  acid  and  of  its  compounds 
presented  a  series  cf  minute  facets,  hitherto  unobserved,  which  made 
them  right-handedly  dissymmetrical.  He  then  went  on  to  examine 
the  tartrates  and  paratartrates  of  ammonia  and  soda,  expecting  to 
find  that  the  tartrates,  like  all  the  others,  were  right-handedly  dis- 
symmetrical, and  that  the  paratartrates,  since  they  caused  no 
rotation  of  the  plane  of  polarization,  were  symmetrical.  The  first 
part  of  his  expectation  was  verified.     But  he  found  that  all  the 


Questions  and  Exercises  493 

crystals  of  the  paratartrate  were  also  dissymmetrical,  but  that 
certain  of  them  were  so  in  one  sense  and  the  others  in  an  opposite 
sense.  It  seemed,  therefore,  that  the  equal  admixture  of  right- 
handed  and  left-handed  crystals  in  the  paratartrate,  the  presence  of 
one  exactly  neutralizing  the  effect  of  the  other,  brought  about  the 
absence  of  rotation  in  the  same  manner  as  the  symmetry  of  all 
would  have  done.     (Ibid.) 

79.  Pasteur  also  noticed  that  one  of  these  two  kinds  of  crystals 
of  the  paratartrate  corresponded  exactly  in  form  with  the  tartrate 
prepared  by  means  of  the  tartaric  acid  of  the  grape.  He  there- 
fore reasoned  that  by  separating  these  by  hand,  he  should  be  able 
to  extract  from  them  by  ordinary  chemical  processes  a  tartaric 
acid  identical  with  that  of  the  grape,  possessing  all  its  physical, 
mineralogical  and  chemical  properties ;  and  that,  per  contra,  from 
the  second  sort  of  crystals  he  should  be  able  to  extract  an  acid 
which  should  also  reproduce  ordinary  tartaric  acid,  save  in  the  one 
circumstance  of  possessing  a  dissymmetry  of  an  inverse  kind  and 
exciting  an  action  equally  inverse  on  polarized  light.  Making 
the  double  experiment,  his  anticipations  were  realized  with  math- 
ematical exactitude.  Before  this,  the  existence  of  two  types  of 
tartaric  acid  was  unknown.     (Ibid.) 

80.  Under  the  same  conditions  of  weight,  temperature,  and  quan- 
tity of  solvent,  Pasteur  placed  successively,  in  presence  of  the  two 
acids,  all  the  substances  capable  of  combining  with  them.  He  found 
that  all  the  resultant  products,  pair  by  pair,  manifested  exactly 
the  same  properties,  both  chemical  and  physical,  with  the  single 
difference  already  exhibited  by  the  two  acids  —  that  in  the  one  case 
the  deviation  of  the  plane  of  polarization  was  to  the  right,  while  in 
the  other  it  was  to  the  left.     (Ibid.) 

81.  The  idea  of  molecular  dissymmetry,  introduced  by  Biot,  was 
forced  upon  Biot's  mind  by  the  discovery  of  a  number  of  liquids,, 
and  of  some  vapors,  which  possessed  the  rotatory  power.  Some, 
moreover,  turned  the  plane  of  polarization  to  the  right,  others  to 


494  Questions  and  Exercises 

the  left.  Crystalline  structure  being  here  out  of  the  question,  the 
notion  of  dissymmetry,  derived  from  the  crystal,  was  transferred  to 
the  molecule.     (Ibid.) 

82.  M.  Pasteur  considers  that  his  researches  point  to  an  irref- 
ragable physical  barrier  between  organic  and  inorganic  nature. 
Never,  he  says,  have  you  been  able  to  produce  in  the  laboratory,  by 
the  ordinary  processes  of  chemistry,  a  dissymmetric  molecule ;  in 
other  words,  a  substance  which,  in  a  state  of  solution,  where  molec- 
ular forces  are  paramount,  has  the  power  of  causing  a  polarized 
beam  to  rotate.  This  power  belongs  exclusively  to  derivatives 
from  the  living  world.  (But  in  a  number  of  cases)  Faraday  caused 
the  plane  of  polarization  in  perfectly  neutral  (i.e.  non-rotating) 
liquids  and  solids  to  rotate.  (And  again),  quartz  as  a  crystal  exerts 
a  very  powerful  twist  on  the  plane  of  polarization.  Quartz  dis- 
solved exerts  no  power  at  all.  The  molecules  of  quartz,  then,  do 
not  belong  to  the  same  category  as  the  crystal  of  which  they  are  the 
constituents;  the  former  are  symmetrical,  thelatter  is  dissymmetrical. 
This,  in  my  opinion,  is  a  very  significant  fact.  By  the  act  of  crystal- 
lization, and  without  the  intervention  of  life,  the  forces  of  molecules 
which  are  symmetrical  are  so  compounded  as  to  build  up  crystals 
which  are  dissymmetrical.  The  reasoning  which  applies  to  the 
dissymmetric  crystal  applies  to  the  dissymmetric  molecule.  The 
dissymmetry  of  the  latter,  however  pronounced  and  complicated, 
arises  from  the  composition  of  atomic  forces  which,  when  re- 
duced to  their  most  elementary  action,  are  excited  along  straight 
lines.     (Tyndall.) 

83.  A  striking  characteristic  of  many  animals,  especially  of  cer- 
tain insects,  is  that  they  resemble  or  mimic  other  animals,  or  even 
inanimate  objects,  in  a  way  that  protects  them  from  the  attacks  of 
enemies,  sometimes  by  making  them  inconspicuous,  sometimes  by 
making  them  appear  dangerous  or  unpalatable.  Four  causes  of 
such  resemblances  have  been  proposed:  (1)  external  or  environ- 
mental causes,  —  food,  climate,  etc. ;    (2)  internal  physiological 


Questions  and  Exercises  49  5 

causes,  compelling  different  species  to  pass  through  similar  phases; 
(3)  sexual  selection;  (4)  natural  selection.  Professor  Poulton, 
examining  the  question,  reasons  as  follows :  — 

(a)  These  resemblances  are  often  to  inanimate  objects,  —  twigs, 
leaves,  earth,  etc.  If  we  admitted  the  action  of  either  internal  or 
external  causes,  they  might,  since  they  would  by  hypothesis  act  alike 
on  the  different  animals,  make  them  resemble  one  another;  but 
it  is  difficult  to  see  why  they  should  make  them  resemble  lifeless 
things.  As  for  sexual  selection,  that  is  exercised  only  at  the  mature 
stage;  and  these-  resemblances  to  inanimate  things  are  very 
common  in  the  immature  stages  of  insects.  Natural  selection, 
however,  explains  all  kinds  of  resemblance  equally  well;  for 
resemblance  to  any  object,  animate  or  inanimate,  which  serves  in 
any  way  to  conceal  or  to  protect  the  animal,  will  be  a  useful  vari- 
ation in  the  struggle  for  life. 

(b)  These  resemblances,  when  between  animals,  are  as  often 
as  not  quite  independent  of  any  affinity  between  the  species ;  e.g. 
the  larva  of  a  moth  looks  like  a  wasp.  But  both  external  and 
internal  causes  would  obviously  produce  the  closest  likeness  where 
there  was  most  physiological  similarity,  i.e.  where  the  species  were 
most  nearly  related. 

(c)  The  resemblances  in  question  are  not  accompanied  by  any 
internal  changes  in  the  direction  of  the  mimicked  species  except 
such  as  assist  in  producing  a  superficial  likeness,  which  is  the  useful 
element  in  the  result.  Natural  selection,  by  its  very  nature,  brings 
about  the  retention  and  accumulation  of  useful  changes  only. 
Physical  and  internal  causes  would  bring  to  pass  changes  of  all 
sorts,  superficial  and  deeply  seated,  indiscriminately. 

(d)  The  same  resemblance  is  often  produced  in  very  different 
ways,  in  different  examples  of  it ;  for  example,  other  insects  mimic 
ants  and  wasps,  sometimes  by  an  actual  likeness  in  form  and  move- 
ment, sometimes  only  by  an  outline  strongly  marked  in  contrasting 
colour  on  bodies  of  very  different  shape.     But  either  a  similar  en- 


496  Questions  and  Exercises 

vironment  or  like  internal  causes  would  bring  these  resemblances 
about,  if  at  all,  in  a  uniform  way.  It  makes  no  difference  to 
natural  selection,  however,  what  the  original  causes  of  a  resem- 
blance are;  if  it  is  useful,  any  change  towards  it  will  be  preserved. 
The  differences  in  the  way  in  which  it  is  produced  will  be  due  to 
the  orginal  differences  in  the  animals 

(e)  The  food  and  conditions  of  life  of  many  of  the  resembling 
species  are  very  different. 

(/)  These  resemblances  are  far  commoner  in  females  than  in 
males.  Yet  there  is  no  assignable  difference  which  would  make 
them  more  responsive  than  the  males  to  the  action  either  of  en- 
vironmental conditions  or  of  internal  causes.  In  fact,  the  female 
usually  varies  less  from  the  ancestral  type  than  the  male.  Such 
resemblances  are  more  useful  to  the  females  than  to  the  males, 
however,  because  of  their  slower  flight  when  laden  with  eggs,  and 
their  greater  exposure  to  attack  during  egg-laying,  incubation,  and 
at  other  times. 

(g)  The  supposed  direct  effect  of  environment  implies  the  inher- 
itance of  acquired  characters,  which  has  never  been  satisfactorily 
proved  to  take  place.     (Poulton,  Essays  on  Evolution,  VIII,  IX.) 

84.  Announcement  was  made  by  Professor  T.  J.  J.  See,  astron- 
omer in  charge  of  the  Naval  Observatory  at  Mare  Island,  that  he 
has  mathematically  proved  that  the  moon  is  a  planet  captured  by  the 
earth  from  space,  and  not  a  detached  portion  of  our  globe.  He  re- 
jects entirely  the  long-accepted  theories  of  Laplace  and  Sir  George 
Darwin  ascribing  earthly  origin  to  the  moon,  and  asserts  that  his 
discovery  is  supported  by  rigorous  mathematical  proof.  Professor 
See's  announcement  was  made  in  a  paper  presented  to  the  meeting 
of  the  Astronomical  Society  of  the  Pacific  Coast,  and  is  a  further 
development  of  his  theory,  promulgated  last  January,  that  all  planets 
and  satellites  are  captured  bodies  which  have  since  had  their  orbits 
reduced  in  size  and  rounded  up  under  the  secular  action  of  the 
nebular-resisting  medium  once  pervading  the  solar  system.     In  his 


Questions  and  Exercises  497 

former  paper  presenting  this  theory  Professor  See  showed  how 
the  satellites,  or  the  material  of  them  which  once  revolved  around 
the  sun,  as  the  asteroids  now  do,  got  shifted  into  orbits  about  the 
planets.  He  has  now  explained  the  origin  of  the  moon  in  the  same 
way,  and  in  his  paper  he  explains  the  famous  outstanding  inequality 
of  six  seconds  in  the  secular  acceleration  of  the  moon's  mean 
motion.  He  says  this  perturbation  in  the  moon's  motion  had 
been  discovered  by  Halley  in  the  time  of  Newton.  It  was 
partially  explained  by  Laplace  in  1787,  but  gravity  alone 
would  not  account  for  the  observed  acceleration  since  the  time 
of  the  Chaldeans,  720  B.C.,  and  the  outstanding  difference  had 
perplexed  the  greatest  mathematicians  for  more  than  a  century. 
Having  discovered  that  the  moon  was  originally  captured  and  was 
still  slowly  nearing  the  earth,  Professor  See  says  he  has  removed  the 
last  difficulty,  and  the  result  would  be  decided  improvement  in 
astronomy.     (N.  Y.  Times.) 

85.  In  1838  Schleiden,  who  had  been  studying  the  cellular 
structure  of  plants  under  the  microscope,  communicated  his  observa- 
tions to  Schwann.  He  mentioned  in  particular  the  nucleus  and 
its  relationship  to  the  other  parts  of  the  cell.  Schwann  was  at 
once  struck  by  the  fact  that  he  had  found  similar  nuclei  in  the 
elements  of  animal  tissue.  Schleiden  also  recognized  these  nuclei 
as  in  effect  the  same  on  being  shown  Schwann's  sections,  and  the 
latter  was  thus  aided  to  come  to  the  conclusion  that  the  elements  in 
animal  tissue  were  practically  identical  with  those  of  plant  tissue. 

86.  In  1835,  before  this  cell  theory  was  announced,  living  matter 
had  been  observed  by  Dujardin.  In  lower  animal  forms  he  noticed 
a  semifluid,  jelly-like  substance,  which  he  designated  sarcode, 
and  which  he  described  as  being  endowed  with  all  the  properties  of 
life.  He  observed  it  very  carefully  in  different  forms  of  the  in- 
vertebrates, not  only  as  to  its  structure,  but  also  as  to  its  chemical 
properties,  which  distinguished  it  from  albumen,  mucus,  gelatin,  and 
other  like  substances.     Dujardin  was  far  from  appreciating  the  full 

2K 


498  Questions  and  Exercises 

mportance  of  his  discovery,  and  for  a  long  time  his  description  of 
sarcode  remained  separate;  but  in  1846  Hugo  von  Mohl,  a 
botanist,  observed  a  similar  jelly-like  substance  in  plants,  which  he 
called  plant-slime,  and  to  which  he  attached  the  name  of  protoplasm. 
On  the  basis  of  these  observations,  and  of  his  own  study  of  the 
movements  of  the  spores  of  one  of  the  simplest  plants,  Cohn,  in 
1850,  declared  that  vegetable  protoplasm  and  animal  sarcode, 
if  not  identical,  were  at  least  in  the  highest  degree  analogous 
substances.  Finally,  in  1861,  Max  Schultze  showed  that  sarcode, 
which  was  supposed  to  be  confined  to  the  lower  invertebrates,  was 
present  also  in  the  tissues  of  higher  animals,  and  there  exhibits  the 
same  properties,  especially  those  of  contractility  and  irritability. 
He  showed  also  that  sarcode  agreed  in  physiological  properties 
with  protoplasm  in  plants,  and  that  the  two  living  substances  were 
practically  identical.  It  was  on  physiological  likeness,  rather  than 
on  structural  or  chemical  grounds,  that  he  based  his  sweeping  con- 
clusions. He  therefore  defined  both  plant  and  animal  cells  as 
little  masses  of  protoplasm  surrounding  a  nucleus. 

87.  On  the  basis  of  continued  microscopic  study  during  the 
years  intervening,  Verworn,  in  1895,  redefined  a  cell  as  "a  body 
consisting  essentially  of  protoplasm  in  its  general  form,  including 
the  unmodified  cytoplasm,  and  the  specialized  nucleus  and  cen- 
trosome;  while  as  unessential  accompaniments  may  be  enumerated 
(1)  the  cell  membrane,  (2)  starch  grains,  (3)  pigment  granules, 
and  (4)  chlorophyl  granules." 

88.  Meanwhile,  the  cell  has  come  to  be  regarded  not  only  as  the 
element  of  structure,  but  also  as  the  unit  of  physiological  activities, 
and  the  conveyer  of  hereditary  qualities.  It  is  seen  that  all  life, 
both  in  plants  and  in  animals,  arises  from  cells;  and  that  where 
sexual  reproduction  takes  place,  in  the  plant  and  the  animal  alike, 
both  the  egg  and  its  fertilizing  agents  are  modified  cells  of  the 
parents'  bodies.  Therefore  the  cell  is  the  only  possible  agent  of 
heredity.    And  by  microscopic  observation  of  fertilized  ova,  it  has 


Questions  and  Exercises  499 

been  determined  that  half  of  their  chromosomes  are  derived  from 
the  male  cell  and  half  from  the  female,  —  each  egg  thus  containing 
hereditary  substance  derived  from  both  parents.  (Locy,  Chs. 
XI,  XII.) 

89.  In  1620  Jean  Tarde  argued  that  because  the  sun  is  "The  eye 
of  the  world,"  and  the  eye  of  the  world  cannot  suffer  from  ophthal- 
mia, sun-spots  must  be  due  not  to  actual  specks  or  stains  on  the 
bright  solar  disk,  but  to  the  transits  of  a  number  of  small  planets 
across  it.  To  this  new  group  of  heavenly  bodies  he  gave  the 
name  of  "Borbonia  Sidera." 

Most  of  those  who  were  capable  of  thinking  at  all  on  such  sub- 
jects adhered  either  to  the  theory  that  the  spots  were  clouds,  or 
that  they  were  slag  thrown  up  in  solar  conflagrations. 

In  the  following  century,  Derham  gathered  from  observations 
carried  on  during  the  years  1703-1711,  "That  the  spots  on  the  sun 
are  caused  by  the  eruption  of  some  new  volcano  therein."  La- 
lande  upheld  the  view  that  the  spots  were  rocky  elevations  uncov- 
ered by  the  casual  ebbing  of  a  luminous  ocean.  This  view  had 
even  less  to  recommend  it  than  Derham's  volcanic  theory.  Both 
were,  however,  significant  of  a  growing  tendency  to  bring  solar 
phenomena  within  the  compass  of  terrestrial  analogies.  (Clerke, 
History  of  Astronomy?) 

90.  In  November,  1769,  a  spot  of  extraordinary  size  engaged 
the  attention  of  Alexander  Wilson,  Professor  of  Astronomy  in  the 
University  of  Glasgow.  He  watched  it  day  by  day,  and  as  the 
great  globe  slowly  revolved,  carrying  the  spot  towards  its  western 
edge,  he  was  struck  with  the  gradual  contraction  and  final  disap- 
pearan^'.  of  the  penumbra  on  the  side  near  the  centre  of  the  disk, 
and  when  on  the  6th  of  December  the  same  spot  reemerged  on 
the  eastern  limb,  he  perceived,  as  he  had  anticipated,  that  the 
shady  zone  was  now  deficient  on  the  opposite  side,  and  resumed 
its  original  completeness  as  it  returned  to  a  central  position. 
Similar  perspective  effects  were  visible  in  numerous  other  spots 


500  Questions  and  Exercises 

subsequently  examined  by  him,  and  he  was  thus  in  1774  able  to 
prove  by  strict  geometrical  reasoning  that  such  appearances  were, 
as  a  matter  of  fact,  produced  by  vast  excavations  in  the  sun's 
substance.  In  1861  De  la  Rue  obtained  a  stereoscopic  view  of  a 
sun-spot  which  confirmed  Wilson's  inference  as  to  their  depressed 
nature.     {Ibid.) 

91.  The  older  explanation  of  fermentation,  espoused  especially 
by  the  great  chemist  Liebig,  was  that  it  was  due  to  the  breaking 
up  of  nitrogenous  substances  under  the  influence  of  the  oxygen 
of  the  air.  "The  ferments,"  said  Liebig,  "are  all  nitrogenous 
substances,  or  the  liquids  which  embrace  them,  in  a  state  of  altera- 
tion which  they  undergo  in  contact  with  the  air."  It  was  further 
noted  that  fermentable  substances  which  had  been  preserved  for 
some  time  unaltered,  in  sealed  vessels,  fermented  at  once  on  expo- 
sure to  the  air. 

Consequently,  when  Cagniard-Latour  and  Schwann  discov- 
ered the  yeast-plant,  Liebig,  carrying  general  opinion  along  with 
him,  contended  that  it  is  not  because  of  its  being  organized  that 
yeast  is  active,  but  because  of  its  being  nitrogenous  substance  in 
contact  with  air.  It  is  the  dead  portion  of  the  yeast  —  that  which 
has  lived  and  is  in  the  course  of  alteration  —  which  acts  upon  the 
sugar,  he  thought.  And  as  in  other  fermentations  the  existence  of 
an  organism  had  not  been  discovered,  its  presence  in  alcoholic 
fermentation  might  be  regarded  as  an  incident  peculiar  to  this. 
(Vallery-Radot,  Louis  Pasteur.) 

92.  It  had  been  noticed  in  Germany  that  a  solution  of  the 
impure  commercial  tartrate  of  lime,  mingled  with  organic  matter, 
fermented  on  being  exposed  to  summer  heat.  On  this  hint, 
Pasteur  prepared  some  pure,  right-handed  tartrate  of  ammonia, 
mixed  with  it  albuminous  matter,  and  found  that  the  mixture 
fermented.  His  solution,  at  first  limpid,  became  turbid.  Search- 
ing for  the  cause  of  the  turbidity,  he  found  it  to  be  due  to  the  multi- 
plication of  a  microscopic  organism,  which  found   in  the   liquid 


Questions  and  Exercises  5QI 

its  proper  food.  Pasteur  held  that  this  organism  was  a  living 
ferment,  a  conclusion  which  was  strengthened,  if  not  prompted, 
by  the  previous  discoveiy  of  the  yeast-plant.     (Tyndall,  ibid.) 

93.  Pasteur  next  performed  a  similar  experiment  with  a  solu- 
tion of  the  paratartrate  of  ammonia.  Owing  to  the  opposition  of 
its  two  classes  of  crystals,  a  solution  of  this  salt,  it  will  be  remem- 
bered, does  not  turn  the  plane  of  polarized  light  either  to  the  left 
or  to  the  right.  Soon  after  fermentation  had  set  in,  a  rotation  to 
the  left  was  noticed.  This  rotation  increased  by  degrees,  and 
reached  its  maximum  at  the  time  that  the  fermentation  was  en- 
tirely completed.  It  was  then  found  that  all  the  right-handed 
tartrate  had  disappeared  from  the  liquid.  The  organism  thus 
proved  itself  competent  to  select  its  own  food.  It  found,  as  it  were, 
one  of  the  tartrates  more  digestible  than  the  other,  and  appropri- 
ated it,  to  the  neglect  of  the  other. 

With  true  scientific  instinct,  Pasteur  closed  with  the  conception 
that  ferments  are,  in  all  cases,  living  things,  and  that  the  substances 
formerly  regarded  as  ferments  are,  in  reality,  the  food  of  the  fer- 
ments. Touched  by  this  wand,  difficulties  fell  rapidly  before  him. 
He  proved  the  ferment  of  lactic  acid  to  be  an  organism  of  a  certain 
kind.  The  ferment  of  butyric  acid  he  proved  to  be  an  organism 
of  another  kind.     (Tyndall,  ibid.) 

94.  In  order  to  prove  his  own  theory,  and  to  disprove  the  asser- 
tion of  Liebig  that  the  presence  of  nitrogenous  albumenoid  matter 
was  essential  to  fermentation,  Pasteur  performed  three  series  of 
experiments:  (1)  The  arguments  of  Liebig  derived  great  strength 
from  the  belief  which  was  shared  by  all  chemists  that  the  cells  of 
yeast  perish  during  fermentation  and  form  lactate  of  ammonia. 
On  examination,  Pasteur  found  that  not  only  was  there  no  am- 
monia formed  during  alcoholic  fermentation,  but  that  even  if 
ammonia  were  added,  it  disappeared,  entering  into  the  formation 
of  new  yeast-cells.  (2)  He  introduced  into  a  pure  solution  of 
sugar  a  small  quantity  of  crystallizable  salts  of  ammonia,  and  some 


$Q2  Questions  and  Exercises 

phosphates  of  potash  and  magnesia.  In  this  solution,  in  which 
nitrogenous  matter  was  not  present,  he  placed  a  minute  quantity  of 
fresh  cells  of  yeast.  The  cells  thus  sown  multiplied,  and  the 
sugar  fermented.  (3)  He  set  up  lactic  acid  fermentation  in 
another  non-nitrogenous  solution.     {Ibid.) 

95.  The  phenomena  of  fermentation  are  in  a  sense  phenomena 
of  nutrition.  The  organism  eats,  if  one  may  say  so,  one  part  of 
the  fermentable  matter.  But  there  is  a  striking  difference  between 
this  and  the  nutrition  of  the  higher  animals,  in  the  fact  that  the 
ferment,  while  nourishing  itself  with  fermentable  matter,  decom- 
poses a  quantity  great  in  proportion  to  its  own  individual  weight. 
In  reflecting  on  this  difference,  it  seemed  to  Pasteur  that  there 
were  two  facts  which  had  much  bearing  upon  it.  It  is  well  known 
that  the  most  vigorous  fermentation,  as,  for  example,  that  of  beer 
or  of  wine,  takes  place  in  vessels  from  which  the  air  is  excluded;  and 
Pasteur  had  discovered  that  the  butyric  acid  ferment  not  only 
lives  without  free  oxygen,  but  is  killed  by  its  admission.  Is  there 
not,  he  asked,  a  relation  between  the  property  of  being  a  ferment 
and  the  faculty  of  living  without  free  oxygen? 

In  order  to  test  this  conclusion,  he  set  up  a  fermentation  of  the 
must  of  beer  and  that  of  grapes  in  shallow  vessels  exposed  to  the 
air.  He  found  that  the  yeast-plant  grew  much  more  than  in  the 
deep  vats,  but  that  the  proportion  of  the  weight  of  the  decomposed 
sugar  to  that  of  the  yeast  formed  was  much  decreased.  While, 
for  example,  in  the  deep  vats  a  kilogram  of  ferment  sometimes 
decomposes  70-150  kilograms  of  sugar,  in  the  shallow  vessel  open 
to  the  air  1  kilogram  of  yeast  corresponds  to  only  5-6  of  decom- 
posed sugar.  In  other  words,  the  more  free  oxygen  the  yeast  fer- 
ment consumes,  the  less  is  its  power  as  a  ferment;  and  the  surplus 
of  material  decomposed,  over  and  above  the  actual  nutriment  of 
the  plant,  must  be  broken  down  by  it  in  order  to  obtain  the  oxygen 
which  it  needs.     (Ibid.) 

96.  Wine  exposed  to  air  becomes  vinegar.     Pasteur  found  that 


Questions  and  Exercises  503 

this  change  was  caused  by  a  small  organism,  the  mycoderma  aceti. 
That  this  organism  was  present  in  the  process  had  long  been 
known,  but  Liebig  denied  that  it  had  anything  essential  to  do  in  it. 
The  true  cause,  he  asserted,  was  the  nitrogenous  matter  present  ip 
the  wine.  In  proof  of  this,  he  pointed  to  the  following  experi- 
ment: If  a  solution  of  pure  alcohol  and  water,  of  the  same  alcoholic 
strength  as  wine,  be  exposed  to  the  air,  even  for  years,  it  will  not 
acetify.  But  if  a  small  quantity  of  any  nitrogenized  substance  be 
added  to  it,  the  change  to  vinegar  then  takes  place. 

Pasteur,  however,  repeated  this  experiment,  adding  to  the  solu- 
tion, instead  of  nitrogenous  substance,  a  small  quantity  of  saline 
crystals  capable  of  sustaining  plant  life.  Acetification  took  place, 
and  the  development  of  the  mycoderm  could  be  seen.     (Ibid.) 

97.  Pasteur  showed  that  oxygen  is  taken  from  the  air  during 
acetification  by  the  following  experiment.  A  bottle  being  par- 
tially filled  with  wine,  and  then  hermetically  sealed,  the  wine 
presently  changes  to  vinegar.  If  the  cork  be  then  withdrawn  under 
the  surface  of  water,  water  rushes  in  to  fill  precisely  one-fifth  of 
the  space  originally  occupied  by  air.  But  air  is  composed  of  one 
part  of  oxygen  to  four  parts  of  nitrogen.  Further  the  gas  left  in 
the  bottle  has  all  the  properties  of  nitrogen.     (Ibid.) 

98.  Newton  showed  that  the  bodies  known  as  comets  obey  the 
law  of  gravitation;  but  it  was  by  no  means  certain  that  the  indi- 
vidual of  the  species  observed  by  him  in  1680  formed  a  permanent 
member  of  the  solar  system.  With  another  comet,  however, 
which  appeared  in  1682,  the  case  was  different.  Edmund  Halley 
calculated  the  elements  of  its  orbit  on  Newton's  principles,  and 
found  them  to  resemble  so  closely  those  arrived  at  for  comets 
observed  by  Peter  Apian  in  1531,  and  by  Kepler  in  1607,  as  almos' 
to  compel  the  inference  that  all  three  apparitions  were  of  a  single 
body.  This  implied  its  revolution  in  a  period  of  about  seventy- 
six  years,  and  Halley  accordingly  fixed  its  return  for  1758-17  59.  It 
punctually  reappeared  on  Christmas  Day,  1758,  and  effected  its 


504  Questions  and  Exercises 

perihelion  passage  on  the  12th  of  March  following,  thus  proving 
beyond  dispute  that  some  at  least  of  these  erratic  bodies  are 
domesticated  within  our  system,  and  strictly  conform  to  its  funda- 
mental laws.     (Clerke.) 

99.  Periodical  comets  are  evidently  bodies  which  have  lived,  each 
through  a  chapter  of  accidents;  and  a  significant  hint  as  to  the 
nature  of  their  adventures  can  be  gathered  from  the  fact  that  their 
aphelia  are  pretty  closely  grouped  about  the  tracks  of  the  major 
planets.  Halley's,  and  four  other  comets,  are  thus  related  to  Nep- 
tune; eight  connect  themselves  with  Uranus,  nine  with  Saturn, 
twenty-five  at  least  with  Jupiter.  Some  form  of  dependence  is 
plainly  indicated,  and  recent  researches  leave  scarcely  a  doubt  that 
the  'capture-theory'  represents  the  essential  truth  in  the  matter. 
The  original  parabolic  paths  of  these  comets  were  then  changed 
into  ellipses  by  the  backward  pull  of  a  planet,  whose  sphere  of 
influence  they  chanced  to  enter  when  approaching  the  sun  from 
outer  space.  Moreover,  since  a  body  thus  affected  should  neces- 
sarily return  at  each  revolution  to  the  scene  of  encounter,  the  same 
process  of  retardation  may,  in  some  cases,  have  been  repeated 
many  times,  until  the  more  restricted  cometary  orbits  were  reduced 
to  their  present  dimensions.     (Ibid.) 

100.  Observations  of  Halley's  comet  have  entirely  disproved 
the  hypothesis  (designed  to  explain  the  invariability  of  the  planetary 
periods)  of  what  may  be  described  as  a  vortex  of  attenuated  matter 
moving  with  the  planets,  and  offering,  consequently,  no  resistance 
to  their  motion.  For  since  Halley's  comet  revolves  in  the  opposite 
direction  to  the  planets,  it  is  plain  that  if  compelled  to  make  head 
against  an  ethereal  current,  it  would  rapidly  be  deprived  of  the 
tangential  velocity  which  enables  it  to  keep  at  its  proper  distance 
from  the  sun,  and  would  thus  gradually  but  conspicuously  ap- 
proach, and  eventually  be  precipitated  upon  it.  No  such  effect, 
however,  has  in  this  crucial  instance  been  detected.     (Ibid.) 

101.  In  1837  Bassi  investigated  the  disease  of  silkworms,  and 


Questions  and  Exercises  50$ 

showed  that  the  transmission  of  that  disease  was  the  result  of  the 
passing  of  minute  glittering  particles  from  the  sick  to  the  healthy. 
Upon  the  basis  of  Bassi's  observation,  the  distinguished  anato- 
mist Henle,  in  1840,  expounded  the  theory  that  all  contagious 
diseases  are  due  to  microscopic  germs. 

The  theory,  however,  was  not  experimentally  proved  until 
1877.  In  that  year  Pasteur  and  Robert  Koch  showed  the  direct 
connection  between  certain  microscopic  filaments  and  the  disease 
of  splenic  fever,  which  attacks  sheep  and  other  cattle.  Koch  was 
able  to  get  some  of  the  minute  filaments  from  diseased  cattle  under 
the  microscope,  and  to  trace  upon  a  warm  stage  the  different 
steps  in  their  germination.  He  saw  the  spores  bud  and  produce 
filamentous  forms.  They  were,  therefore,  living  organisms. 
He  was  able  to  cultivate  these  upon  a  nutrient  substance,  gelatin, 
and  in  this  way  to  obtain  a  pure  culture  of  the  organism,  which  is 
called  anthrax.  He  inoculated  mice  with  the  pure  culture  of 
anthrax  germs,  and  produced  splenic  fever  in  the  inoculated.  He 
was  able  to  do  this  through  several  generations  of  mice.     (Locy.) 

102.  Koch  insisted  that  there  are  four  necessary  steps  in  the 
proof  that  any  organism  is  the  cause  of  a  particular  disease.  These 
are:  First,  that  a  microscopic  organism  of  a  particular  type  should 
be  found  in  great  abundance  in  the  blood  and  the  tissue  of  the  sick 
animal;  second,  that  a  pure  culture  should  be  made  of  the  sus- 
pected organism;  third,  that  this  pure  culture,  when  introduced 
into  the  body  of  another  animal,  should  produce  the  disease ;  and 
fourth,  that  in  the  blood  and  tissues  of  that  animal  there  should  be 
found  quantities. of  the  suspected  organism.     (Ibid.) 

103.  Koch  found  that,  while  guinea-pigs,  mice,  and  other  ani- 
mals were  killed  by  inoculation  with  anthrax,  birds  were  not 
affected.  This  invulnerability  had  very  much  struck  Pasteur 
and  his  two  assistants.  What  was  it  in  the  body  of  a  fowl  that 
enabled  it  thus  to  resist  inoculations  of  which  the  most  infini- 
tesimal quantity  sufficed  to  kill  an  ox  ?     They  proved  by  a  series 


506  Questions  and  Exercises 

of  experiments  that  the  microbe  of  splenic  fever  does  not  develop 
when  subjected  to  a  temperature  of  440  Centigrade.     Now,  the 
temperature  of  birds  being  between  41  and  420,  may  it  not  be,, 
said  Pasteur,  that  the  fowls  are  protected  from  the  disease  because 
their  blood  is  too  warm?     Might  not  the  vital  resistance  encoun- 
tered in  the  living  fowl  suffice  to  bridge  over  the  small  gap  between 
41-420,  and   44-450  ?  .  .  .     This  idea  conducted  Pasteur  and  his 
assistants  to  new  researches.     'If  the  blood  of  a  fowl  were  cooled,' 
they  asked,   'could  not  the  splenic    fever   parasite  live  in  this 
blood  ?'     The  experiment  was  made.      A  hen  was  taken,  and 
after  inoculating  it  with  splenic  fever  blood,  it  was  placed  with 
its  feet  in  water  at  250.     The  temperature  of  the  blood  of  the  hen 
went  down  to  37  or  380.     At  the  end  of  twenty-four  hours  the  hen 
was  dead,  and  all  its  blood  was  filled  with  splenic  fever  bacteria. 
But  if  it  was  possible  to  render  a  fowl  assailable  by  splenic  fever 
simply  by  lowering  its  temperature,  is  it  not  also  possible  to  restore 
to  health  a  fowl  so  inoculated  by  warming  it  up  again  ?     A  hen 
was  inoculated,  subjected,  like  the  first,  to  the  cold-water  treat- 
ment, and  when  it  became  evident  that  the  fever  was  at  its  height 
it  was  taken  out  of  the  water,  wrapped  carefully  in  cotton  wool, 
and  placed  in  an  oven  at  a  temperature  of  350.     Little  by  little 
its  strength  returned ;  it  shook  itself,  settled  itself  again,  and  in  a 
few  hours  was  fully  restored  to  health.     The  microbe  had  disap- 
peared.    Hens  killed  after  being  thus  saved,  no  longer  showed  the 
slightest  trace  of    splenic  organisms.      There    have  been   great 
discussions  in  Germany  and  France  upon  a  mode  of  treatment  in 
t/phoia  fever,  which  consists  in  cooling  the  body  of  the  patient 
by  frequently  repeated  baths.     The  possible  good  effects  of  this 
treatment  may  be  understood  when  viewed  in  conjunction  with  the 
foregoing  experiment  on  fowls.     In  typhoid  fever  the  cold  arrests 
the  fermentation,  which  may  be  regarded  as  at  once  the  expres- 
sion and  the  cause  of  the  disease,  just  as,  by  an  inverse  process, 
the  heat  of  the  body  arrests  the  development  of  the  splenic  fever 
microbe  in  the  hen.     (Vallery-Radot,  Louis  Pasteur.) 


Questions  and  Exercises  507 

104.  In  1865  Pasteur  undertook  the  investigation  of  the  silk- 
worm disease  which  was  ruining  the  silk  industry  of  France.  The 
presence  of  vibratory  corpuscles  in  the  blood  of  the  diseased 
worms  was  already  known,  and  he  was  prepared  by  his  previous 
discoveries  of  the  micro-organisms  which  cause  fermentation  to 
see  in  these  corpuscles  the  cause  of  the  disease. 

By  the  use  of  the  microscope,  he  secured  a  number  of  healthy 
worms,  free  from  corpuscles.  He  prepared  two  infusions,  one  by 
pounding  up  a  diseased  worm  in  water,  the  other  by  pounding  up 
a  healthy  worm.  These  infusions  were  then  brushed  over  mul- 
berry leaves,  separately,  and  the  healthy  worms  were  allowed  to 
feed,  some  on  the  first  bed  of  leaves,  the  others  on  the  second. 
The  first  group  of  worms  became  diseased,  the  second  remained 
healthy. 

It  was  further  established,  by  observation  of  the  diseased  worms, 
that  in  the  first  stages  of  the  disease,  when  they  cannot  readily  be 
distinguished  from  the  healthy,  these  corpuscles  are  confined  to  the 
intestines.  As  the  disease  progresses  and  becomes  obvious,  they 
are  found  in  the  other  tissues;  and  at  death  the  body  is  full  of 
them. 

Separating,  therefore,  the  uninfected  moths  from  the  infected, 
by  the  use  of  the  microscope,  taking  care  that  the  food  should  be 
free  of  infection,  the  progeny  of  the  former  were  found  to  be 
always  free  from  the  disease,  and  that  of  the  latter  to  be  always 
diseased.     (Vallery-Radot,  Louis  Pasteur.) 

105.  The  first  to  employ  the  prism  in  the  examination  of  various 
flames  was  a  young  Scotchman  named  Thomas  Melvill.  He 
studied  the  spectrum  of  burning  spirits,  into  which  were  intro- 
duced successively  sal  ammonia,  potash,  etc.,  and  noticed  the 
singular  predominance,  under  almost  all  circumstances,  of  a  par- 
ticular shade  of  yellow  light,  taking  up  a  perfectly  definite  and 
invariable  position  in  the  spectrum.  Fraunhofer,  the  great 
Munich  optician,  later  rediscovered  Melvill 's  deep  yellow  ray  and 


508  Questions  and  Exercises 

measured  its  place  in  the  colour  scale.  It  has  since  become  well 
known  as  the  'sodium  line,'  and  has  played  a  very  important 
part  in  the  history  of  spectrum  analysis.  Nevertheless,  its 
ubiquity  and  conspicuousness  long  impeded  progress. 

It  was  because  of  this  perplexing  fact  that  Fox  Talbot  hesitated 
in  1826  to  announce  his  theory  that  the  presence  in  the  spectrum 
of  any  individual  ray  told  unerringly  of  the  volatilization  in  the 
flame  under  scrutiny  of  some  body  as  whose  badge  or  distinctive 
symbol  that  ray  might  be  regarded.  The  yellow  ray  appeared 
indeed  without  fail  where  sodium  was;  but  it  also  appeared  where 
it  might  be  thought  only  reasonable  to  conclude  that  sodium  was 
not.  Nor  was  it  until  thirty  years  later  that  William  Swan,  by 
pointing  out  the  extreme  delicacy  of  the  spectral  test,  and  the 
singularly  wide  dispersion  of  sodium,  made  it  appear  probable 
(but  even  then  only  probable)  that  the  questionable  yellow  line 
was  really  due  invariably  to  that  substance.  Common  salt  (chlo- 
ride of  sodium)  is,  in  fact,  the  most  diffusive  of  solids.  It  floats 
in  the  air;  it  flows  with  water;  every  grain  of  dust  has  its  attend- 
ant particle;  its  absolute  exclusion  approaches  the  impossible. 
And  withal,  the  light  that  it  gives  in  burning  is  so  intense  and  con- 
centrated, that  if  a  single  grain  be  divided  into  180  million  parts, 
and  one  alone  of  such  inconceivably  minute  fragments  be  present  in 
a  source  of  light,  the  spectroscope  will  show  unmistakably  its 
characteristic  beam.     (Clerke.) 

106.  In  1859  Kirchhoff  and  Bunsen  entered  on  a  long  series  of 
stringent  and  precise  experiments,  as  a  result  of  which  they  were 
able  to  state  positively  that  certain  rays  in  the  spectrum  are  neces- 
sarily and  invariably  connected  with  certain  kinds  of  matter. 
The  assurance  of  their  conclusion  was  rendered  doubly  sure  by  the 
discovery,  through  the  peculiarities  of  their  light  alone,  of  two 
new  metals,  named  from  the  blue  and  red  rays  by  which  they 
were  respectively  distinguished,  'Caesium'  and  'Rubidium.' 
Both   were  immediately  afterwards  actually  obtained  in  small 


Questions  and  Exercises  509 

quantities  by  evaporation  of  the  Diirkheim  mineral  waters. 
(Ibid.) 

Fraunhofer  in  181 5,  by  means  of  a  slit  and  a  telescope,  made  the 
surprising  discovery  that  the  solar  spectrum  is  crossed,  not  by 
seven,  but  by  thousands  of  obscure  transverse  streaks.  Of  these 
he  counted  some  600,  and  carefully  mapped  324.  The  same  sys- 
tem of  examination  applied  to  the  rest  of  the  heavenly  bodies 
showed  the  mild  effulgence  of  the  moon  and  the  planets  to  be  defi- 
cient in  precisely  the  same  rays  as  sunlight;  while  in  the  stars  it 
disclosed  the  differences  in  likeness  which  are  always  an  earnest 
of  increased  knowledge. 

One  solar  line  especially  —  that  marked  in  his  map  with  the 
letter  D  —  proved  common  to  several  of  the  stars  examined ;  and 
it  was  remarkable  that  it  exactly  coincided  in  position  with  the  con- 
spicuous yellow  beam  which  he  had  already  found  to  accompany 
most  kinds  of  combustion.  Moreover,  both  the  dark  solar  and  the 
bright  terrestrial  'D-lines'  were  displayed  by  his  refined  appliances 
as  double.  In  this  striking  correspondence  was  contained  the  very 
essence  of  solar  chemistry ;  but  its  true  significance  did  not  become 
apparent  until  long  afterwards.     (Ibid.) 

107.  The  'fixed  lines '  (as  they  were  called)  of  the  solar  spectrum 
took  up  the  position  of  a  standing  problem.  One  view  was  that  the 
atmosphere  of  the  earth  was  the  agent  by  which  sunlight  was 
deprived  of  its  missing  beams.  For  some  of  them  this  is  actually  the 
case.  Brewster  found  in  1832  that  certain  dark  lines,  which  were 
invisible  when  the  sun  stood  high  in  the  heavens,  became  in- 
creasingly conspicuous  as  he  approached  the  horizon.  These  are 
the  well-known  '  atmospheric  lines ' ;  but  the  immense  majority  of 
their  companions  in  the  spectrum  remain  quite  unaffected  by  the 
thickness  of  the  stratum  of  air  traversed  by  the  sunlight  containing 
them.     (Ibid.) 

108.  There  remained  the  true  interpretation  —  absorption  in 
the  sun's  atmosphere;   and  this,   too,  was  extensively  canvassed 


510  Questions  and  Exercises 

But  a  remarkable  observation  made  by  Professor  Forbes  of  Edin* 
burgh  on  the  occasion  of  the  annular  eclipse  of  May  15,  1836, 
appeared  to  throw  discredit  upon  it.  If  the  problematical  dark 
lines  were  really  occasioned  by  the  stoppage  of  certain  rays  through 
the  action  of  a  vaporous  envelope  surrounding  the  sun,  they 
ought,  it  seemed,  to  be  strongest  in  light  proceeding  from  his  edges, 
which,  cutting  that  envelope  obliquely,  passed  through  a  much 
greater  depth  of  it.  But  the  circle  of  light  left  by  the  interposing 
moon,  and  of  course  derived  entirely  from  the  rim  of  the  solar  disk, 
yielded  to  Forbes's  examination  precisely  the  same  spectrum  as 
light  coming  from  its  more  central  parts.  This  circumstance 
helped  to  baffle  inquirers,  already  sufficiently  perplexed.  It  still 
remains  an  anomaly,  of  which  no  complete  explanation  has  been 
offered.     (Ibid.) 

109.  Convincing  evidence  as  to  the  true  nature  of  the  solar  lines 
was  however  at  length,  in  the  autumn  of  1859,  brought  forward  at 
Heidelberg.  Kirchhoff 's  experiment  in  the  matter  was  a  very  simple 
one.  He  threw  bright  sunshine  across  a  space  occupied  by  vapour 
of  sodium,  and  perceived  with  astonishment  that  the  dark  Fraun- 
hofer  line  D,  instead  of  being  effaced  by  flame  giving  a  luminous 
ray  of  the  same  refrangibility,  was  deepened  and  thickened  by  the 
superposition.  He  tried  the  same  experiment,  substituting  for 
sunbeams  light  from  a  Drummond  lamp,  and  with  similar  result. 
A  dark  furrow,  corresponding  in  every  respect  to  the  solar  D-line, 
was  instantly  seen  to  interrupt  the  otherwise  unbroken  radiance  of 
its  spectrum.  The  inference  was  irresistible,  that  the  effect  thus 
produced  artificially  was  brought  about  naturally  in  the  same  way, 
and  that  sodium  formed  an  ingredient  in  the  glowing  atmosphere 
of  the  sun. 

This  first  discovery  was  quickly  followed  up  by  the  identification 
of  numerous  bright  rays  in  the  spectra  of  other  metallic  bodies 
with  others  of  the  hitherto  mysterious  Fraunhofer  lines.  Kirchhoff 
was  thus  led  to  the  conclusion  that  (besides  sodium)  iron,  magne- 


Questions  and  Exercises  ^l\ 

»ium,  calcium,  and  chromium  are  certainly  solar  constituents,  and 
that  copper,  zinc,  and  nickel  are  also  present,  though  in  smallei 
quantities. 

These  memorable  results  were  founded  upon  a  general  principle 
first  enunciated  by  Kirchhoff,  which  maybe  expressed  as  follows: 
Substances  of  every  kind  are  opaque  to  the  precise  rays  which  they 
emit  at  the  same  temperature;  that  is  to  say,  they  stop  the  kinds  of 
light  or  heat  which  they  are  then  actually  in  a  condition  to 
radiate.     (Ibid.) 

no.  When  a  tree,  or  a  bundle  of  wheat  or  barley  straw,  is  burnt, 
a  certain  amount  of  mineral  matter  remains  in  the  ashes  —  ex- 
tremely small  in  comparison  with  the  bulk  of  the  tree  or  of  the 
straw,  but  absolutely  essential  to  its  growth.  In  a  soil  lacking,  or 
exhausted  of,  the  necessary  mineral  constituents,  the  tree  cannot 
live,  the  crop  cannot  grow.  Now  contagia  are  living  things,  which 
demand  certain  elements  of  life  just  as  inexorably  as  trees,  or 
wheat,  or  barley;  and  it  is  not  difficult  to  see  that  a  crop  of  a  given 
parasite  may  so  far  use  up  a  constituent  existing  in  small  quantities 
in  the  body,  but  essential  to  the  growth  of  the  parasite,  so  as  to 
render  the  body  unfit  for  the  production  of  a  second  crop.  The 
soil  is  exhausted,  and,  until  the  lost  constituent  is  restored,  the  body 
is  protected  from  any  further  attack  of  the  same  disorder.  Such 
an  explanation  of  non-recurrent  diseases  naturally  presents  itself 
to  a  thorough  believer  in  the  germ  theory.  .  .  .  To  exhaust  a  soil, 
however,  a  parasite  less  vigorous  and  destructive  than  the  really 
virulent  one  may  suffice;  and  if,  after  having  by  means  of  a  feebler 
organism  exhausted  the  soil,  without  fatal  result,  the  most  highly 
virulent  parasite  be  introduced  into  the  system,  it  will  prove  power- 
less. This,  in  the  language  of  the  germ  theory,  is  the  whole  secret  of 
vaccination.  (Tyndall.)  Have  you  any  remarks  to  make  on  this 
explanation  ? 

in.  A  great  number  of  contagious  diseases  are  non-recurrent; 
an  individual  who  has  had  one  of  them  once  is  not  likely  to  have  it 


512  Questions  aud  Exercises 

again.  What  explanation  can  be  given  of  this  fact?  or  of  the  fact 
that  vaccination,  itself  a  disease,  preserves  from  the  smallpox? 
After  dwelling  long  on  these  facts  this  question  arose  in  Pasteur's 
mind :  If  contagious  maladies  do  not  repeat  themselves,  why  should 
there  not  be  found  for  each  of  them  a  disease  different  from  them, 
but  having  some  likeness,  which,  acting  upon  them  as  cow-pox 
does  upon  smallpox,  would  have  the  virtue  of  a  prophylactic? 

In  experimenting  with  successive  cultures  of  the  fowl  cholera 
germ,  he  found  that  while  those  made  at  short  intervals  killed  the 
birds  inoculated  with  it  within  twenty-four  or  forty-eight  hours,  a 
culture  which  had  remained  for  three  months  in  a  flask  with  a 
stopper  of  cotton  wool,  which  allows  nothing  but  pure  air  to  pass 
through  it,  not  only  did  not  kill  the  birds  inoculated  with  it,  but 
that  when  such  birds  were  reinoculated  with  fresh  and  strong  virus 
they  did  not  die.  The  conclusion  was  simple:  the  disease  can 
protect  from  itself.  It  has  evidently  that  characteristic  of  virulent 
diseases,  that  it  cannot  attack  a  second  time.  Pasteur  had  suc- 
ceeded in  producing  a  vaccine  for  fowl  cholera.     (Vallery-Radot.) 

112.  What  is  it  that  weakens  the  virus  during  the  interval 
intentionally  placed  between  two  successive  cultivations,  so  as  to 
produce  the  vaccine  ?  The  oxygen  of  the  air.  For  if  the  cultiva- 
tion of  this  microbe  is  carried  on  in  a  tube  containing  very  little 
air,  and  if  the  tube  is  then  closed  by  the  flame  of  a  lamp,  the  mi- 
crobe, by  its  development  and  life,  quickly  appropriates  all  the 
free  oxygen  contained  in  the  tube,  as  well  as  the  oxygen  dissolved 
in  the  liquid.  Thus,  completely  protected  from  contact  with 
oxygen,  the  microbe  does  not  become  sensibly  weakened  for 
months,  sometimes  for  years.     (Ibid.) 

113.  Pasteur  now  turned  his  attention  to  discovering,  if  possible, 
a  similar  vaccine  against  splenic  fever  in  cattle.  In  the  course  of 
his  investigations  he  discovered  that  this  disease  was  non-recurrent, 
and  he  was  therefore  confident  that  such  a  vaccine  could  be  found. 
He  cultivated  the  microbe,  and  exposed  it  to  the  oxygen  o'f  the  air 


Questions  and  Exercises  513 

at  a  temperature  which  prevented  the  formation  of  spores  —  for 
these  would  protect  it  from  the  oxygen.  The  resulting  weakened 
culture  protected  the  animals  inoculated  with  it  from  the  fever. 
114.  Pasteur's  discovery  of  a  splenic  fever  protective  virus 
was  doubted,  and  on  the  invitation  of  an  Agricultural  Society  he 
performed  a  public  experiment  at  Melun.  On  May  5,  1881, 
24  sheep,  6  cows,  and  1  goat  were  inoculated  with  five  drops  of 
an  attenuated  splenic  virus.  On  May  17  they  reinoculated 
these  31  animals  with  an  attenuated  virus,  which  was,  however, 
stronger  than  the  preceding  one.  Finally,  on  May  31,  very 
virulent  inoculation  was  administered  to  these  31  animals,  and 
also  to  25  sheep  and  4  cows  which  had  not  previously  been  inocu- 
lated. On  June  2,  out  of  the  25  sheep  which  had  not  been  vac- 
cinated, 21  were  dead;  the  goat  was  also  dead;  2  other  sheep  were 
dying,  and  the  last  was  certain  to  die  that  evening.  The  non-vac- 
cinated cows  had  all  voluminous  swellings  at  the  point  of  inocula- 
tion, behind  the  shoulder.  The  fever  was  intense,  and  they  had  no 
longer  strength  to  eat.  The  vaccinated  sheep  were  in  full  health. 
The  vaccinated  cows  showed  no  tumour;  they  had  not  even 
suffered  an  elevation  of  temperature,  and  they  continued  to  eat 
quietly.     (Ibid.) 

PART    III.  —  The  Nature  of  Thought 
Chapter  XXI.  —  Judgment  the  Elementary  Process 

1    What  objections  are  there  to  speaking  of  thought  as  'a  thing 
like  other  things'  ? 

2.  What  is  the  general  law  of  Evolution  ?    Explain  what  is 
meant  by  a  change  from  the  homogeneous  to  the  heterogeneous. 

3.  What  general  conclusions  are  reached  by  the  application  of 
the  law  of  Evolution  to  the  thought-process  ? 

4.  What   do   you    understand   by   Judgment  ?    How   does   a 
simple  judgment  differ  from  sensation  ? 

3L 


514  Questions  and  Exercises 

5.  In  what  sense  may  our  judgments  be  said  to  be  the  union 
of  two  concepts? 

6.  Would  the  doctrine  that  in  knowing  we  first  have  Simple 
Apprehension,  then  as  separate  intellectual  processes,  Judgment 
and  finally  Inference,  agree  with  the  general  evolutionary  view 
of  consciousness?     Explain  fully. 

Chapter  XXII.  —  The  Characteristics  of  Judgment 

1.  What  do  you  understand  by  the  universality  of  judgments  ? 
What  is  the  distinction  between  the  universality  of  a  judgment 
and  that  of  a  proposition? 

2.  How  would  you  prove  that  all  judgments  are  universal? 

3.  Is  any  judgment  necessary  in  itself?  If  not,  whence  do 
judgments  derive  their  necessity? 

4.  What  is  the  argument  by  which  it  has  been  maintained  that 
there  must  be  judgments  or  principles  which  are  in  themselves 
necessary?     How  would  you  reply  to  this  argument? 

5.  Explain  how  it  is  possible  for  a  judgment  to  be  at  once  both 
analytic  and  synthetic. 

6.  Explain  what  is  meant  by  a  'system'  of  knowledge. 

7.  When  judgment  brings  new  facts  into  relation  to  what  we 
already  know,  does  the  old  body  of  knowledge  itself  undergo 
any  modification? 

Chapter  XXIII.  —  The  Laws  of  Thought 

1.  In  what  sense  can  we  speak  of  a  law  of  Thought? 

2.  Explain  what  is  meant  by  the  law  of  Identity. 

3.  How  has  this  law  been   interpreted  by  Boole  and  Jevons  ? 

4.  What  does  Jevons  mean  by  the  'substitution  of  similars,' 
and  how  does  he  propose  to  employ  this  principle  ? 

5.  What  objections  are  there  to  employing  the  sign  of  equality 
to  represent  the  relation  between  the  subject  and  predicate  of  a 
judgment? 


Questions  and  Exercises  5 1  *j 

6.  Explain  how  the  law  of  Identity  is  related  to  the  character- 
istics of  judgment  treated  in  the  last  chapter. 

7.  What  is  the  meaning  of  the  law  of  Contradiction? 

8.  Explain  the  use  of  the  law  of  Excluded  Middle. 

9.  In  what  general  postulate  of  thought  is  the  meaning  of  all 
these  laws  included? 

Chapter  XXIV.  —  Types  of  Judgment 

1.  Why  do  we  begin  with  judgments  of  Quality  ? 

2.  Explain  how  we  pass  in  the  development  of  intelligence 
from  Quality  to  Quantity. 

3.  In  what  sense  is  it  true  that  judgments  of  Quantity  never 
give  us  the  real  nature  of  things,  but  only  their  relation  to  some- 
thing else  ? 

4.  What  is  meant  by  anthropomorphic  causes?  How  are 
they  distinguished  from  scientific  causes?  What  is  meant  by 
Animism  ? 

5.  What  new  element  did  the  discovery  of  the  law  of  the  Con- 
servation of  Energy  introduce  in  the  causal  conception  as  em- 
ployed in  certain  sciences? 

6.  Why  cannot  this  new  extension  have  any  application  in  the 
field  of  the  mental  sciences? 

7.  How  does  the  standpoint  of  judgments  of  Individuality 
differ  from  that  of  judgments  of  Causality?  What  is  meant  by 
an  '  infinite  regress '  ? 

Chapter  XXV.  —  Inference 

1.  How  does  Inference  differ  from  Judgment?  In  what  sense 
may  it  be  said  that  it  is  an  extension  of  the  latter  process? 

2.  Does  the  passage  from  Judgment  to  Inference  illustrate  the 
general  law  of  Logical  Evolution?     Explain. 

3.  In  the  development  of  our  knowledge,  which  usually  comes 
first,  premises  or  conclusion? 


5 16  Questions  and  Exercises 

4.  How  is  it  possible  to  pass  from  the  known  to  the  unknown? 

5.  Explain  under  what  circumstances  only  an  Inference  is 
possible. 

6.  What  is  the  common  element  in  both  Induction  and  Deduc- 
tion?   How  do  they  differ? 

Chapter    XXVI.  —  The  Unification  of  Knowledge 

1.  Explain  the  distinction  between  '  Science  '  and  'the  sciences.' 

2.  What  part  does  philosophy  play  in  the  progress  of  knowledge 
toward  unity? 

3.  Why  would  it  be  unsatisfactory  to  construct  a  philosophy 
simply  by  taking  as  ultimate  the  most  general  laws  and  principles 
of  physical  science  ?  Can  you  mention  any  philosophers  who  have 
proceeded  in  this  way? 

4.  What  is  meant  by  the  abstract  or  hypothetical  character  of 
the  special  sciences?  Illustrate  in  the  case  of  physics  and  psy- 
chology. 

5.  Do  the  various  sciences  differ  in  their  degree  of  abstract- 
ness  ?  If  so,  how  would  you  classify  them  in  order  of  concrete- 
ness?     Compare  mathematics  and  biology  in  this  respect. 

6.  Explain  the  function  of  philosophy  as  the  interpretation  of 
the  results  of  the  sciences. 

7.  What  is  meant  by  the  statement  that  philosophy  must  find 
a  new  category  or  principle  of  synthesis?  Illustrate  by  showing 
what  categories  might  conceivably  be  employed  by  philosophy. 


INDEX 


Abstract,  two  Meanings  of  the  Word,  I  Cant  Words  and  Phrases,  302 


51  ff 

Accent,  the  Fallacies  of,  168. 

Accident,  the  Fallacy  of,  178  f. 

A  fortiori  Arguments,  141. 

Agreement,  the  Method  of,  2^g;  Defi- 
ciencies in  the  Method  of,  242-243. 

Amphiboly,  the  Fallacy  of,  168. 

Analogy,  Explanation  by  Means  of, 
266:  the  Principle  of,  268;  State- 
ments of  Law,  269;  its  Func- 
tion in  suggesting  Hypothesis,  271; 
its  Use  by  Darwin,  272;  its  Incom- 
pleteness as  a  Method  of  Explanation, 
274. 

Analysis,  its  Relation  to  Synthesis,  279. 

Analytic  Procedure,  135  f. 

Anthropomorphism,  364. 

A  priori  Truths,  334. 

Argument,  Irregular  Forms  of,   133  ff. 

Argumenlum,  ad  rem,  184;  ad  homi- 
nem,  184  f-;  ad  poputum,  185;  ad  igno- 
rantiam,  186;  ad  verecundiam.  186; 
ad  misericordiam,  185;  ad  baculum, 
187. 

Aristotle,  Logic  of,  23;  List  of  Logical 
Works,  23;  his  Theory  of  the  Syllo- 
gism, 23;  as  Founder  of  Modern 
Sciences,  23;  Importance  of  In- 
duction and  Deduction  in  his  Logic, 
25 ;  his  Classification  of  Fallacies,  164; 
his  Statement  of  the  Law  of  Con- 
tradiction, 350. 

Art,  an,  its  Relation  to  a  Science,  9  f. 


I? 


Bacon,  Logic  of,  28;  his  Method,  28; 
on  Induction  by  Simple  Enumeration, 
193;  on  the  Tendency  to  neglect 
Negative  Instances,  310;  his  Doctrine 
of  the  Four  Idols,  310-14  f. 

Bosanquet,  his  remarks  on  Analogy, 
276. 

Bradley,  13. 


Causal    Connection,    as    Principle    of 

Science,  235  f.;   Judgments  of,  362  ff. 
Cause,  the  Fallacy  of  the  False,    189; 

the  Development  of  the  Principle  of, 

362  ff. 
Causes,  the  Plurality  of,  244. 
Chances,  the  Calculation  of,  228. 
Circle,  Argument  in  a,  181. 
Classification,  Principles  of,  79;    Rules 

of,  81;    of  Fallacies,  165,  299;   Aris- 
totle's, of  Fallacies,  164. 
Composition,  the  Fallacy  of,  i74f. 
Concepts,   Relation    to    Percepts    and 

Judgments,  44  ff.,  324  ff. 
Conclusion,  the  Irrelevant,  182. 
Concrete,  two  Senses  of  the  Word,  51. 
Connotation,  of  Terms,  58  ff. 
Consequent,  Fallacy  of  the,  187. 
Conservation  of   Energy,  the   Law  of, 

and  its  Influence  on  the  Conception 

of  Cause,  366. 
Contradiction,  the  Law  of,  38,  350. 
Conversion,  the,  of  Propositions,   105; 

Simple,    101;     by    Limitation,    106; 

Errors  in,  167. 


D 


Darwin,  his  Power  of  arresting  Excep- 
tions, 263;  his  Use  of  Analogy, 
272;  his  Employment  of  Hypotheses, 
281. 

Deduction,  its  Relation  to  Induction, 
384. 

Definuion,  the  Necessity  of,  64;  Verbal 
and  Real,  66;  Ways  ot  Regarding, 
67;  Socrates'  Search  for,  685  Rules 
of,  70;    Genetic,  74  ff. 

Denotation,  of  Terms,  5Sff.:  Descartes, 

So- 
Dialectic,  Socrates'  Use  of,  68. 
Dichotomy.  77. 
Difference,  Method  of,  244  f. 
Differentia,  70. 


5?7 


5i8 


Index 


Dilemma,  the  Simple  Constructive,  157; 
the  Complex  Constructive,  158; 
the  Simple  Destructive,  157;  the 
Complex  Destructive,  159;  the  Fal- 
lacies of,  161  ff.,  179. 

Division,  Rules  for,  81;  the  Fallacy  of, 
176. 

E 

Eduction,  99. 

Elimination,  the  Part  of,  in  Induction, 
199,  289. 

Enthymemes,  40,  133. 

Enumeration,  as  the  Starting-point  of 
Induction,  194,  217;  Judgments  of, 
359- 

Episyllogisms  and   Prosyllogisms,    134. 

Equivocation,  the  Fallacies  of,  172. 

Ethics,  its  Standpoint  compared  with 
that  of  Psychology,  372. 

Euler,  92. 

Evolution,  the  Law  of,  315;  the  Appli- 
cation of  the  Law  of,  to  Thought, 
317  ff. 

Excluded  Middle,  the  Law  of,  77,  352. 

Experiment  and  Observation,  197; 
Advantages  of  employing,   211. 

Explanation  and  Observation,  207  f. ; 
the  Problem  oi,  212. 

Extension  and  Intension  of  Terms,  55. 


Fallacies,  Classification  of,  165,  299; 
Syllogistic,  165;  Inductive,  298;  the 
Source  of,  298;  of  Interpretation, 
166;  occasioned  by  Language,  299: 
of  Reasoning,  170,  309;  of  Observa- 
tion, 303;    Individual,  312. 

Figures  of  the  Syllogism,  120;  the 
Special  Canons  of  the  four,  123;  De- 
termination of  the  Valid  Moods  in, 
127;  the  Perfect,  130;  the  Imperfect, 
130;  Reduction  of,  130;  the  Organic 
Relation  of,  132  note. 


Galen,  130. 

Generalization,  Danger  of  hasty,  310  f. 

Genus,  its  Definition,  70. 

Guericke,  287. 

H 

Hegel,  his  Influence  on  the   Develop- 
ment of  Logic,  32. 


Herschel,  J.,  31. 

Hypothesis,  as  guiding  Induction,  201^ 
Reasoning  from  an,  278;  the  Employ- 
ment of,  to  explain  Common  Events, 
279;  Darwin's  Use  of,  281;  the 
Necessity  for  an,  282;  Formation  of, 
282  f.;  the  Function  of  Analogy  in 
suggesting,  200,  2S4;  the  Proof  of,  285 
ff.;  Requirements  of  a  Good,  293  ff. 


Identity,  the  Law  of,  38,  343;  Jev- 
ons's  Interpretation  of  the  Law  of, 
344. 

Ignoratio  Elenchi,  182. 

Imagination,  its  Part  in  the  Formation 
of  Theories,  282. 

Individuality,  Judgments  of,  370. 

Induction  and  Deduction,  384;  the 
Baconian  Method  of,  28;  Mill's 
Emphasis  on,  31;  the  Problem  of, 
190  f.;   Perfect  and  Imperfect,  193  f. 

Inference,  Mediate  and  Immediate,  97; 
the  Nature  of,  378;  as  distinguished 
from  Judgment,  373;  the  Paradox 
of,  379;  as  a  Development  of  Judg- 
ment, 378.    (See  also  Reasoning.) 

Instances,  the  Value  of  Numerous,  i96f. 

Intension  and  Extension  of  Terms,  58  ff. 

Interpretation,  of  Propositions,  97  ff.; 
Errors  of,  166;  Judgment  a  Process 
of,  322. 

J 

James,  9: 

Jevons,  his  Account  of  Perfect  Induc- 
tion, 193;  his  Calculation  of  Chances, 
228;  his  Interpretation  of  the  Law 
of  Identity,  344;  his  Principle  of  the 
Substitution  of  Similars,  345. 

Judgment,  Relation  to  Perception  and 
Conception,  44  ff.,  324  ff.;  the  Start- 
ing-point of  Knowledge,  322;  as  a 
Process  of  Interpretation,  323;  and 
Concept,  324;  the  Universality  of,  329; 
the  Necessity  of,  331;  a  priori,  334; 
as  involving  both  Analysis  and  Syn- 
thesis, 334  ff.;  as  constructing  a  Sys- 
tem of  Knowledge,  339;  its  Relation 
to  Inference,  373. 

Judgments,  of  Quality,  355;  of  Quan- 
tity, 358;  of  Enumeration,  359;  of 
Measure,  360;  of  Causal  Connec- 
tion, 362 ;  of  Individuality,  370. 


Index 


519 


Language,  Relation  to  Thought,  3  f., 
46,  326;  Dangers  from  the  Careless 
Use  of,  64,  298;  Fallacies  of,  299; 
Figurative,  302. 

Law,  of  Identity,  38,  343;  of  Contra- 
diction, 38,  350;  of  Excluded  Mid- 
dle, 77,  352;  of  Conservation  of 
Energy,  367. 

Laws  of  Thought,  38,  77,  343;  on  the 
Careless  Use  of  Words,  64,  300. 

Logic,  Definition  of,  1 ;  Derivation  of 
the  Word,  3;  Relation  to  Psychol- 
ogy. 5!  Relation  to  Rhetoric,  3  f . ; 
Comparison  with  Physiology,  7;  as 
Normative  Science,  6,  14;  as  a 
Science  and  an  Art,  9;  Utility  of,  11 ; 
Necessity  of,  13:  the  Materials  of, 
14;  of  the  Sophists,  20;  of  Socrates, 
20;  of  Aristotle,  23,  36;  of  the  School- 
men. 27;  ot  Bacon,  28;  of  Mill,  31, 
34;  Development  of  Modern,  ^2; 
the  Equation.il,  344. 

Lyell,  his  Overthrow  of  the  'Catas- 
trophic' Theory  in  Geology,  296. 


M 


Malthus,   his  Theories  of   Population, 

183,  273. 
Measure,  Judgments  of,  360. 
Metaphors,  Dangers  from  the  Use  of, 

3°3- 

Method,  the  Progressive  or  Synthetic, 
135;  the  Regressive  or  Analytic,  135; 
the,  of  Agreement,  239;  the,  of  Dif- 
ference, 244;  the  joint,  of  Agreement 
and  Difference,  249;  the,  of  Con- 
comitant Variations,  255;  the,  of 
Residues,  260. 

Middle  Term,  the  Function  of  the,  113; 
Ambiguous,  171. 

Mill,  his  Importance  in  the  History  of 
Logic,  31;  his  Experimental  Meth- 
ods, 237. 

Mnemonic  Lines,  for  Syllogism,  129. 

Moods,  of  Syllogism,  121. 

Morphology,  compared  with  Psychol- 
ogy. 7- 

N 

Negative  Instances,  Tendency  to  neg- 
lect, 304. 


Neptune,  the  Discovery  of,  264. 
Newton,  his  Care  in  testing  Theories, 

288. 
Non  sequitur,  187. 
Normative  Science,  Logic  as,  6,  14. 

O 

Observation,  and  Explanation,  207  ff.; 
and    Experiment,    211;     Errors    of, 

3°3- 
Obversion,    the,   of   Propositions,    103; 

Errors  in,  167. 
Opposition,  the,  of  Propositions,  99. 


Perception,  Relation  to  Conception  and 
Judgment,  44  ff.;  as  involving  Judg- 
ment, 45,  325;  Difficulty  in  distin- 
guishing between  Inference  and,  308. 

Petitio  Principii,  180. 

Philosophy  and  Science,  390;  as  inter- 
pretation of  the  sciences,  405. 

Physiology  compared  with  Logic,  7. 

Plato,  in  the  History  of  Logic,  23;  and 
the   Doctrine  of  Reminiscence,   380. 

Post  hoc  propter  hoc,  189,  310. 

Fredicables,  the,  69. 

Prejudices,  Individual,  312;  of  an  Age, 

3J3- 

Premises,  Definition  of,  40. 

Presumption,  Fallacies  of,  180. 

Propositions,  Categorical,  85;  Condi- 
tional, 85;  the  Nature  of,  84;  Qual- 
ity and  Quantity  of,  86;  Difficul- 
ties in  classifying,  89;  Relation  of 
Subject  and  Predicate  in,  90;  the 
Opposition  of,  99;  Contrary  and 
Contradictory,  100;  the  Obversion 
of,  103;  the  Conveision  of,  105;  the 
Contraposition  of,  107;  the  Inver- 
sion of,  109. 

Prosyllogisms,  134. 

Psychology,  its  Relation  to  Logic,  5; 
Comparison  with  Morphology,  7; 
Comparison  with  Ethics,  372. 


Quality,    of    Propositions,    86;     Judg- 

ments  of,  355. 
Quantity,   of   Propositions,   86;    Judg* 

ments  of,  358. 


520 


Index 


Quaternio  Tcr  minor  urn,  170. 

Question,  the  Fallacy  of  the  Complex, 

181. 
Question-Begging  Epithet,  301. 


R 


Reasoning,  the  Nature  of  Syllogistic, 
112;  Mediate,  97,  113;  Immediate, 
97;  Mistakes  in,  309;  Inductive  and 
Deductive,  384;  from  Particulars  to 
Particulars,  384;  from  Particulars  to 
a  Universal,  388.  (See  also  Infer- 
ence.) 

Reduction  of  the  Imperfect  Figures, 
130. 

Residues,  the  Method  of,  260. 


Scepticism,  of  the  Sophists,  20  ff.,  330. 

Schonbein,  his  Discovery  of  Ozone, 
263. 

Science,  as  related  to  Art,  9;  as  related 
to  Philosophy,  390;  as  Philosophy, 
395;   the  Assumptions  of,  399. 

Sigwart,  on  the  Difference  between 
Ancient  and  Modern  Science,  219; 
on  the  Application  of  Statistics,  220. 

Similars,  the  Principle  of  the  Substitu- 
tion of,  345. 

Socrates,  his  Place  in  the  History  of 
Logic,  20;  his  Search  for  Definitions, 
68;   his  Employment  of  Dialectic,  68. 

Sophists,  the  Logic  of,  20;  Socrates' 
Refutation  of,  22;  Plato's  Criticism 
of  their  Theory  of  Knowledge,  2y, 
their  Scepticism,  330. 

Sorites,  Aristotelian,  137;  Goclenian, 
138. 

Species,  Definition,  70. 

Statistics,  219. 

Subject,  Relation  of  Predicate  and,  90. 


Syllogism,  the  Aristotelian,  23,  36;  thft 
Nature  of  the,  36;  the  Principle  of 
the,  37;  the  Parts  of  the,  39;  the 
Rules  of  the,  115;  the  Figures  of  the, 
120;  the  Hypothetical,  143;  Rules 
for  the  Hypothetical,  145;  Relation 
of  Categorical  and  Hypothetical,  148; 
the  Disjunctive,  154;  Fallacies  of  the 
Disjunctive,  156. 

Synthesis,  its  Relation  to  Analysis,  334. 

Synthetic  Procedure,  135  f. 

System,  Difference  between  a,  and  an 
Aggregate,  339. 


Terms,  Definition  of  Logical,  49; 
Singular  or  Individual,  49;  General 
and  Collective,  49;  Abstract  and 
Concrete,  51  ff.;  Positive  and  Nega- 
tive, 55;  Contradictory  and  Con- 
trary, 56  f. ;  Privative,  56;  Absolute 
and  Relative,  57;  Extension  and 
Intension  of,   58  ff. 

Thales,  365. 

Thought,  its  Relation  to  Language,  3  f., 
46,  326;  the  Laws  of,  38,  77,  343; 
as  a  process  of  Transformation  and 
Conservation,  47  f ;  the  Nature  of,  316. 

Torricelli,  287. 

U 

Unification  of  Knowledge,  390. 
Uniformity  of  Nature,  203,  236. 


Variations,    of     Statistics,     225; 
Method  of  Concomitant,  255. 

W 

Whewell,  16,  206. 

Words,  the  Abuse  of,  65,  a88. 


th« 


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